The kinetic energy of the roller coaster at the bottom of the hill is 1800 joules, which is indeed twice the kinetic energy at the top of the hill (450 joules). This confirms the statement that the car has joules of kinetic energy at the bottom of the hill, which is twice its kinetic energy at the top.
The kinetic energy of the roller coaster at the bottom of the hill is twice its kinetic energy at the top of the hill.
To find the kinetic energy (KE) of the roller coaster, we use the formula:
[tex]\[ KE = \frac{1}{2}mv^2 \][/tex]
where [tex]\( m \)[/tex] is the mass of the object and [tex]\( v \)[/tex] is its velocity.
Given that the mass [tex]\( m \)[/tex] of the roller coaster car is 100 kilograms, and its speed [tex]\( v \)[/tex] at the top of the hill is 3 meters/second, we can calculate the kinetic energy at the top of the hill as follows:
[tex]\[ KE_{top} = \frac{1}{2} \times 100 \text{ kg} \times (3 \text{ m/s})^2 \] \[ KE_{top} = \frac{1}{2} \times 100 \text{ kg} \times 9 \text{ m}^2/\text{s}^2 \] \[ KE_{top} = 50 \text{ kg} \times 9 \text{ m}^2/\text{s}^2 \] \[ KE_{top} = 450 \text{ J} \][/tex]
Since the speed of the roller coaster car doubles at the bottom of the hill, its new speed [tex]\( v_{bottom} \)[/tex] is:
[tex]\[ v_{bottom} = 2 \times 3 \text{ m/s} = 6 \text{ m/s} \][/tex]
The kinetic energy at the bottom of the hill is:
[tex]\[ KE_{bottom} = \frac{1}{2} \times 100 \text{ kg} \times (6 \text{ m/s})^2 \] \[ KE_{bottom} = \frac{1}{2} \times 100 \text{ kg} \times 36 \text{ m}^2/\text{s}^2 \] \[ KE_{bottom} = 50 \text{ kg} \times 36 \text{ m}^2/\text{s}^2 \] \[ KE_{bottom} = 1800 \text{ J} \][/tex]
Therefore, the kinetic energy of the roller coaster at the bottom of the hill is 1800 joules, which is indeed twice the kinetic energy at the top of the hill (450 joules). This confirms the statement that the car has joules of kinetic energy at the bottom of the hill, which is twice its kinetic energy at the top.
The cunninghams are moving across the country. Mr.cunningham leaves 2.5 hours before mrs.cunningham. If he averages 40 mph and she averages 65 mph,how long will it take Mrs.cunningham to overtake mr.cunningham?
When she starts out, he is (40x2.5)= 100 miles ahead of her.
She gains (65-40)= 25 miles on him every hour.
It takes her (100/25)= 4 hours to catch up to him.
It will take Mrs. Cunningham 4 hours to overtake Mr. Cunningham.
To determine how long it will take Mrs. Cunningham to overtake Mr. Cunningham, use the following steps:
1. Calculate the distance Mr. Cunningham travels before Mrs. Cunningham starts:
Distance = Speed × Time [tex]\[ \text{Distance} = 40 \text{ mph} \times 2.5 \text{ hours} = 100 \text{ miles} \][/tex]2. Determine the relative speed at which Mrs. Cunningham is gaining on Mr. Cunningham:
Relative speed = Mrs. Cunningham's speed - Mr. Cunningham's speed [tex]\[ \text{Relative speed} = 65 \text{ mph} - 40 \text{ mph} = 25 \text{ mph} \][/tex]3. Calculate the time it takes for Mrs. Cunningham to cover the distance between them at the relative speed:
Time = Distance / Relative speed[tex]\[ \text{Time} = \frac{100 \text{ miles}}{25 \text{ mph}} = 4 \text{ hours} \][/tex]Every object that has mass attracts every other object with a gravitational force. It has been proven that the size of the gravitational force increases as the objects’ masses increase but graviational force decreases rapidly as the distance between the objects increases.
This statement about matter and its behavior is best classified as a
fairlr accurate one .........
Answer:
It is Law/C.
Explanation:
I did the test. ✔
How is electron movement related to the bonding in sodium chloride? A) The atomic orbitals overlap and share electrons causing an ionic bond to form. B) Electrostatic sharing of electrons between atoms allows covalent bond formation. C) Electrons exchange creating ions to form an ionic bond by electrostatic attraction. D) Orbital overlap occurs between the atoms to exchange electrons to form the covalent bond.
Answer: Option (C) is the correct answer.
Explanation:
Sodium has atomic number 11 and its electronic distribution is 2, 8, 1. Whereas chlorine has atomic number 17 and its electronic configuration is 2, 8, 7.
Therefore, we can see that sodium has one extra electron and chlorine has deficiency of one electron.
So, in order to complete their octet sodium will give its one valence electron to the chlorine atom. Hence, there is exchange of electrons and thus it will result in the formation of ionic bond.
Thus, we can conclude that in sodium chloride electron movement is related to the bonding as electrons exchange creating ions to form an ionic bond by electrostatic attraction.
Answer:
Its C
Explanation: just had it on usatestprep
Find the length of this regular solid. The total volume is 104 cm3. What is the length of the rectangular prism? cm
Answer: 4 cm
Explanation:
Which of the following represents the most powerful earthquake? Kuril Islands, 8.5 Great Chilean, 9.5 San Francisco, 7.8 Prince William Sound, 9.2
The answer is Great Chilean, 9.5.
Answer:
Great Chilean, 9.5
Explanation:
Great Chilean earth quake also known as 1960 Valdivia earthquakes. It is the most powerful earthquake ever which is recorded on 22 May 1960.
Various studies suggests that it is placed at between 9.4–9.6 on the scale of magnetic moment.
It occurred in the afternoon and last long for about 10 minutes of period. Then the resulting Tsunami affects the Southern Chile, Japan, Hawaii, the Philippines, Eastern New Zealand and Southern Australia.
And the epicenter of this earthquake is about 570 km.
The atomic number of yttrium is 39. The atomic mass of one of its isotopes is 89. How many neutrons are in an atom of this isotope?
The number of neutron in the atom of the isotope is 50.
What are isotopes?Isotopes are different nuclear species—technically, nuclides—of the same element. They both belong to the same chemical element and have the same atomic number (number of protons in their nuclei), but they have distinct nucleon numbers (mass numbers) because they have different numbers of neutrons in their nuclei.
Although the chemical properties of all isotopes of a given element are almost identical, their atomic weights and physical characteristics vary.
The atomic mass of yttrium atom of the isotope is = 89
The atomic number of yttrium atom is = 39
Hence, the proton number of the atom of the isotope is = 39
Total number of proton and neutron in the atom of the isotope is = 89
Therefore, the number of neutron in the atom of the isotope is = 89 -39 = 50.
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the fastest airplane is the lockheed sr 71 blackbird a high altitude spy plane first built in 1964. if an sr-71 is clocked traveling 15.0 km west in 15.3 s, what is its average velocity in kilometers per hours
For the motion of the plane it is given to us that it travel 15.0 km in 15.3 s
So here we can use the formula of average velocity to find it
formula is given as ratio of total displacement and total time
[tex]v = \frac{displacement}{time}[/tex]
here it is given that
[tex]displacement = 15.0 km[/tex]
time = 15.3 s
we need to convert the time into hour as the speed is required in km/h
so we know that
[tex]1 h = 3600 s[/tex]
[tex]t = 15.3 s * \frac{1h}{3600 s}[/tex]
[tex]t = 4.25 * 10^{-3} h[/tex]
now by the above formula
[tex]v = \frac{15.0}{4.25 * 10^{-3}}[/tex]
[tex]v = 3529.4 km/h[/tex]
so the velocity of the plane would be 3529.4 km/h
What is 17.857142 repeating, times 68.6?
it equals 1224.9999412
What are the physical properties of gases
if your run at 12 m/s for 15 minutes, how far will you go?
HURRY!!!!!!!!!!!
If the macaroni’s mass is 200 grams, what is the density? (Use the volume you calculated in 7a) Be sure to show your work and label all units.
The density of a substance is the ratio of its mass to its volume. So whatever volume you have (call it [tex]V[/tex]), the density [tex]\rho[/tex] is computed by
[tex]\rho=\dfrac{200\,\mathrm g}V[/tex]
The density of the macaroni cannot be calculated without knowing the volume. If volume is available, density can be computed by dividing mass by volume.
Explanation:In the realm of Physics, density is determined by the ratio of mass to volume, typically in units of grams per cubic centimeter (g/cm³). To find the density of an object, you simply divide the mass by the volume. However, in the context of your question, we are not provided with the volume calculated in question 7a.
Without the volume, the calculation of density can't be completed. If we have the volume, the formula to calculate the density would be Density = Mass / Volume. So for example, if the macaroni's volume was 50cm³, then the density would be 200g / 50cm³ = 4g/cm³.
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Where are the magnetic fields stronger near a bar magnet?
A) Top
B) Center
C) Ends
D) Bottom
your answer is c) Ends
As can be visualized with the magnetic field lines, the magnetic field is strongest inside the magnetic material. The strongest external magnetic fields are near the poles. A magnetic north pole will attract the south pole of another magnet, and repel a north pole.
Answer: The correct answer is "Ends".
Explanation:
Bar magnet is a permanent magnet.
Bar Magnet has two poles: North pole and South pole.
Same poles repel each other and the opposite poles attract each other.
The magnetic field lines originates from the north pole and ends at the south pole.
The magnetic filed lines are surrounding of the magnet in which the magnetic force can be experienced. The magnetic fields are stronger near the poles of the magnet. As the distances decreases from the poles, the magnetic fields lines get weaker.
Therefore, the correct option is (C).
A mountain climber packs too much gear and finds it difficult to reach the summit before a storm blows in. How does this scenario demonstrate Newton’s law
newtons law states gravity holds things down there fore wigheing you down
Answer:
The greater force will be required to overcome weight.
Explanation:
According to Newton’s second law of motion:
F = W = mg ………. (i)
Equation (i) shows that with the increase in mass the force or weight in the downward direction will increase. When climber packs too much gear then he has to apply more force in the upward direction to overcome his on weight and luggage. Therefore, it will be difficult for him to reach the summit before a storm blows in. In this way, this scenario is related with Newton’s law.
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you put a screw in a wall stud with a screw driver.
then you put a screw in the wall with an electric screw driver.
which of the following statements is true?
a. less work is done with the electric screw driver.
b. the same work was done, but the electric screw driver increased the rate of work.
c. the same work was done, but the electric screw driver decreased the rate of work.
d. more work was done because the electric screw driver was more powerful.
A screwdriver is used to insert a screw into a wall stud. Then, using an electric screwdriver, you drive into the wall. The identical task was done, but the electric screwdriver sped up the process.
An electric screwdriver is a portable tool that allows the user to screw/ unscrew. It's head is outfitted with a bit holder, that can be magnetic or have a quick-release mechanism. A screwdriver should be a must tool in just about any toolbox. It can be used to manually push screws into a range of surfaces such as walls, wood, metal, or porcelain. It is typically used by hand and turn screws with slotted heads.Therefore, the answer is "Option b".
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The statement which is true about using both a screw driver and an electric screw driver to put a screw in a wall stud is: B. the same work was done, but the electric screw driver increased the rate of work.
Work can be defined as a measure of energy transfer that takes place when an object is moved due to the application of a force along a displacement.
Hence, the work done by an object is the multiplication (product) of the perpendicular force acting on the object and the distance it covers.
Mathematically, work done is given by the formula:
[tex]Work\;done = Force \times displacement[/tex]
Generally, a screw driver and an electric screw driver can be used to perform the same work of put a screw in a wall stud.
However, an electric screw driver has a motor, which makes the speed (work rate) of putting a screw in the wall faster than a screw driver.
Additionally, a screw driver is a mechanical tool and as such it requires more human effort to put a screw in a wall stud, thereby, decreasing the rate of work.
In conclusion, the same work was done by using both a screw driver and an electric screw driver, but the electric screw driver increased the rate of work.
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Why would an object float in water, but sink in rubbing alcohol?
Because water is more dense than the object but rubbing alcohol is less dense than the object
An object floats or sinks based on the densities of the object and the fluid. Water's higher density and surface tension compared to rubbing alcohol enables certain objects to float in it but sink in rubbing alcohol.
Explanation:The object's ability to float or sink in a fluid depends on the densities of the object and the fluid. If the object's average density is less than that of the fluid it will float. This is because the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force which equals the weight of the fluid displaced is thus greater than the weight of the object. On the other hand, an object denser than the fluid will sink.
Water has a higher density than rubbing alcohol thus objects that can float in water may sink in rubbing alcohol if their density is greater than that of the alcohol. Additionally liquids such as water exhibit properties such as cohesion and surface tension which can support objects denser or heavier than the water to some extent until the surface tension is broken. However the surface tension of rubbing alcohol is significantly lower than that of water affecting the floating capability of the object.
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Vinegar (C2H4O2) and baking soda (NaHCO3) react to form sodium acetate, water, and carbon dioxide. C2H4O2 + NaHCO3 ? How many total oxygen atoms are expected in these products? A. 2 B. 3 C. 4 D. 5
The total oxygen atoms that are exprected in the vinegar and baking soda reaction is three oxygen atoms.
Answer: B. 3
why;live
Answer: D. 5
Explanation:
According to the law of conservation of mass, mass can neither be created nor be destroyed. Thus the mass of products has to be equal to the mass of reactants. The number of atoms of each element has to be same on reactant and product side. Thus chemical equations are balanced.
The balanced chemical equation will be:
[tex]C_2H_4O_2+NaHCO_3\rightarrow CH_3COONa+H_2O+CO_2[/tex]
Thus there are 2 atoms of oxygen in vinegar and 3 atoms of oxygen in baking soda. Which means there are 5 oxygen atoms on reactant side.
Thus the products must also have 5 oxygen atoms.
A student is walking along the hallway at 1m/s when the bell rings for class. The student reaches their classes their classroom door in 10 seconds ,now moving at 3m/s. How much did they accelerate
The student accelerated at a rate of 0.2 m/s², calculated using the final and initial velocities, and the time taken to change velocity.
Explanation:To calculate the acceleration of the student moving from 1 m/s to 3 m/s in 10 seconds, we can use the formula for acceleration, which is Δv/Δt, where Δv is the change in velocity and Δt is the time taken to change the velocity.
Here, the initial velocity (u) is 1 m/s, the final velocity (v) is 3 m/s, and the time (t) is 10 seconds. The change in velocity (Δv) is v - u = 3 m/s - 1 m/s = 2 m/s. The time (Δt) is 10 seconds. Therefore, the acceleration (Δv/Δt) is 2 m/s / 10 s = 0.2 m/s².
The student therefore accelerated at 0.2 m/s².
Bambi the young dear was distracted Buy butterfly and jumped into the road in front of the two vehicles as shown in the diagram below both drivers were distracted and so did not see Bambi and not break or change velocity in any way. Car a is 70 miles per our heading east and is 350 m away from Bambi. Carpet is 50 mph heading west and is 590 feet away from Bambi. Who will hit Bambi first?
Speed of car A is given as
[tex]v_a = 70 mph[/tex]
now we need to convert it into SI units
1 miles = 1609 m
1 hour = 3600 s
now we have
[tex]v_a = 70 *\frac{1609}{3600} = 31.3 m/s[/tex]
now its distance from Bambi is given as
[tex]d_a = 350 m[/tex]
time taken by it to hit the Bambi
[tex]t = \frac{d}{v}[/tex]
[tex]t = \frac{350}{31.3}[/tex]
[tex]t = 11.2 s[/tex]
Now other car is moving at speed 50 mph
so its speed in SI unit will be
[tex]v_b = 50* \frac{1609}{3600}[/tex]
[tex]v_b = 22.35 m/s[/tex]
now its distance from Bambi is given as
[tex]d_b = 590 feet[/tex]
as we know that 1 feet = 0.3048 m
[tex]d_b = 590*0.3048 = 179.83 m[/tex]
now the time to hit the other car is
[tex]t_2 = \frac{179.83}{22.35}[/tex]
[tex]t_b = 8.05 s[/tex]
So Car B will hit the Bambi first
Answer:
Car b
Explanation:
A jewellery melts 500g of Silver to pour into a mould. Calculate how much energy was released as the silver solidified.
When silver is poured into the mould the it will solidify
In this process the phase of the Silver block will change from liquid to solid.
This phase change will lead to release in heat and this heat is known as latent heat of fusion.
The formula to find the latent heat of fusion is given as
[tex]Q = mL[/tex]
here given that
[tex]m = mass = 500 g[/tex]
[tex]L = 111 kJ/kg[/tex]
now we can find the heat released
[tex]Q = 0.5 * 111 kJ[/tex]
[tex]Q = 55.5 kJ[/tex]
So it will release total heat of 55.5 kJ when it will solidify
Across a resistor, the potential:
increases
decreases
remains constant
Final answer:
Across a resistor in a circuit, the potential decreases due to the resistance. This potential drop is determined by the current in the circuit and the resistance value according to Ohm's Law (V = IR).
Explanation:
Across a resistor, the potential decreases. This is because the resistor causes a potential drop, which is the product of the current flowing through the resistor and the resistance of the resistor (Ohm's Law, V = IR). If we consider a simple electrical circuit where current flows from a battery through a resistor, as the current "passes through" the battery, the potential of the electrical energy increases by a value V, representing the voltage of the battery.
However, as the current then "passes through" the resistor, the potential energy of the charges is converted into other forms of energy like heat, leading to a decrease in potential by the value given by the product of the current (I) and the resistance (R) of the resistor.
The wires connecting the components in the circuit, assuming they have negligible resistance, do not cause a significant change in voltage. Therefore, as current travels through these wires, the voltage remains constant.
Match the term with the definition. (4 points)
1. Element
2. Atom
3. Particle
4. Phase
a. the basic unit of an element
b. a substance that cannot be broken down into a simpler substance
c. a tiny piece of matter
d. a unique form of matter in which it can exist
Element is is a substance that cannot be broken down into a simpler substance
Atom is the basic unit of an element
Particle a tiny piece of matter
A phase is a unique form of matter in which it can exist
What is the matter?Anything which has mass and occupies spaces is known as matter, mainly there are four states of matter solid liquid gases, and plasma.
These different states of matter have different characteristics according to which they vary their volume and shape.
Unable to be reduced to a simpler substance, an element is a substance.
An element's fundamental unit is the atom, and a particle is a small piece of matter.
An exclusive state of matter is referred to as a phase.
Thus, an Element is a substance that cannot be broken down into a simpler substance, Atom is the basic unit of an element, a Particle a tiny piece of matter, and a phase is a unique form of matter in which it can exist
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a rock is dropped from a bridge. what happens to the magnitude of the acceleration and the speed of the rock as it falls?
a) both acceleration and speed increase
b) both acceleration and speed remain the same
c) acceleration increases & speed decreases
d) acceleration remains the same & speed increases
If a rock is dropped from a bridge, its acceleration remains the same (9.8 m/s², the acceleration of gravity on Earth, no matter how heavy the rock is), and its speed increases at the rate of (9.8 meters per second for every second it falls).
The acceleration of the rock remains the same while the speed increases as the rock moves downwards.
The motion of an object dropped from a certain height is affected by Earth's gravitational influence.
The acceleration due gravity on the object will be constant throughout the motion. The direction of this acceleration due to gravity is downwards.The object's speed increases as the object moves downwards and it will eventually become maximum before the object hits the ground.
The direction of the object's speed is always in the direction of the object's motion.Thus, we can conclude that the acceleration of the rock remains the same while the speed increases as the rock moves downwards.
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0.8mj of energy are used by a blender in 3 and a half minutes. What is the power rating of the oven
Given that 0.8 MJ of energy is used in 3.5 minute of time
Now we need to find the power rating
so here power consumed is given by rate of energy which is defined by formula
[tex]Power = \frac{Energy}{time}[/tex]
now we will plug in all given data
[tex]Energy = 0.8 MJ = 8 * 10^5 J[/tex]
[tex]time = 3.5 min = 3.5 * 60 = 210 s[/tex]
now we will find the power
[tex]P = \frac{8 * 10^5}{210}[/tex]
[tex]P = 3809.5 Watt[/tex]
[tex]P = 3.81 kW[/tex]
so it will consume total 3.81 kW power
Final answer:
The power of a blender that uses 0.8MJ in 3.5 minutes is approximately 3.81kW. To find the power rating of an oven, however, additional information would be required.
Explanation:
To calculate the power rating of an oven that uses 0.8 megajoules (MJ) of energy in 3.5 minutes, we would first convert the energy to joules (J), since 1 MJ = 1,000,000 J. Therefore, the energy used is 0.8 MJ * 1,000,000 J/MJ = 800,000 J. After that, we need to convert the time to seconds for consistency since power is typically measured in watts (J/s). There are 60 seconds in a minute, so 3.5 minutes * 60 seconds/minute = 210 seconds.
Now we can calculate the power using the formula: Power (P) = Energy (E) / Time (t). Plugging in our values gives us P = 800,000 J / 210 s = 3,809.52 watts or approximately 3.81 kilowatts (kW). However, since we are looking for the power rating of the oven and not the blender.
You've slammed on the brakes and your car is skidding to a stop while going down a 20∘ hill. Identify all the forces acting on the car.
There will be the following forces:
Force of gravity directly down.
The normal force perpendicular to the hill.
The braking force directed uphill.
The frictional force directed uphill.
All components of the force acting on the car are:
• The Normal force perpendicular to the surface of the car.
• The force of gravity in downhill direction.
• The breaking force in the uphill direction.
• The friction force in the uphill direction.
Further Explanation:
Free body diagram is the graphical representation or illustration of all the forces applied on the body with their directions. This helps us to visualize all the applied forces on the body with their directions and make us possible to solve complex problems based on kinematics.
Given:
The inclination of the road is [tex]20^\circ[/tex].
Concept:
The free body diagram is drawn as shown in Figure 1.
The car is moving on incline hill making an angle [tex]20^\circ[/tex] with the plane surface. When sudden break is applied to the car it skids to some distance. As soon as the brakes are applied, the car experiences a friction force due to brakes and starts slowing down.
The friction force offered by the hill is dependent on the normal force which is equal to the component of the weight acting perpendicular to the road.
The coefficient of static friction [tex]\mu[/tex] is depend upon the nature of surface of the irregularities. The friction force acts in the direction opposite to the motion.
The car has its normal force and it is the component of the contact force which is always perpendicular to the surface of the object.
The car has component of the force in the downward direction along the hill due to gravity called as weight. It’s magnitude depend upon the mass of the body and expressed as [tex]mg[/tex]. the term [tex]g[/tex] is called acceleration due to gravity and it has a constant value of [tex]9.81\text{ m/s}^2[/tex].
Therefore, the all the force acting on the car are given below.
• The Normal force perpendicular to the surface of the car.
• The force of gravity in downhill direction.
• The breaking force in the uphill direction.
• The friction force in the uphill direction.
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Answer Details:
Grade: Middle school
Subject: Physics
Chapter: Kinematics
Keywords:
Friction, acceleration, slammed, break, car, skidding, net stop, going down, 20degree, hill, components, force, force acting on car, weight, normal.
Which of the following are true about centripetal force? Check all that apply. A. Without centripetal force, an object cannot accelerate. B. Friction can be a centripetal force, such as when it keeps a car on the road going around a curve. C. Gravity can be a centripetal force, such as when it pulls a satellite in its orbit. D. It's also called an outward force.
B. Friction can be a centripetal force, such as when it keeps a car on the road going around a curve.
C. Gravity can be a centripetal force, such as when it pulls a satellite in its orbit.
Explanation:
The centripetal force is any force that keeps an object moving in circular motion, "pulling" the object towards the centre of the circular trajectory.
Several forces can act as centripetal force. Examples are:
- friction: when a car is going around the curve, is moving by circular motion. The force that keeps the car in circular motion is, in fact, the friction between the tires and the road.
- Gravity: when a satellite moves around the Earth, it is moving by circular motion. The force that keeps the satellite in circular motion is the gravitational attraction between the Earth and the satellite, that pushes the satellite towards the Earth.
The other two options are not correct because:
A) An object can also accelerate if there is no centripetal force (for example, a car speeding up on a straight road is accelerating, but there is no centripetal force since there is no circular motion
D) Centripetal force is not an outward force, since it pushes the object inwards (towards the centre of the trajectory).
How do I find the direction of the velocity and acceleration ?
The mainly three types of directions exits between velocity and acceleration.
ExplanationThe velocity and acceleration are the vector quantities as having both magnitude and direction. To direction of both factors depends upon the speed. for example, we take a car to observe the direction of these two factors, then there will be no direction when the car is at rest.
When the car moves at uniform velocity then its direction will be forward but there will be no direction of acceleration.
When the car moves with increasing speed continuously, then the direction of velocity and acceleration will be parallel.
When the car is at speed and trying to slow down its speeds, it will create acceleration. In this case, the direction of velocity and acceleration will be in the opposite.
Help? Will give thanks if right (thank you)
The cheetah can maintain its maximum speed for only 7.5 s. What is the minimum distance the gazelle must be ahead of the cheetah to have a chance of escape? (After 7.5 s the speed of cheetah is less than that of the gazelle.) Answer in units of m.
Final answer:
The minimum distance the gazelle must be ahead of the cheetah to have a chance of escape is 112.5 m.
Explanation:
To find the minimum distance the gazelle must be ahead of the cheetah, we need to calculate the distance the cheetah covers in 7.5 seconds when it reaches its maximum speed.
Using the formula:
Displacement = Initial velocity * Time + (1/2) * Acceleration * Time^2
Since the cheetah starts from rest, its initial velocity is 0 m/s. The acceleration is not given in the question, so we can't calculate the exact distance. However, we can use the example provided, where the cheetah accelerates at 4 m/s², to illustrate the calculation.
Let's assume the cheetah's acceleration is 4 m/s². Plugging in the values:
Displacement = (0 m/s) * (7.5 s) + (1/2) * (4 m/s²) * (7.5 s)^2
Displacement = 0 + (1/2) * 4 m/s² * 56.25 s²
Displacement = 0 + 2 * 56.25 m = 112.5 m
Therefore, the minimum distance the gazelle must be ahead of the cheetah is 112.5 meters.
What insight does Williams provide regarding future space travel?
A physics book is thrown horizontally at a velocity of 5.0 m/s from the top of a cliff 78.4 m high. How long does the book take to reach the bottom of the cliff .
The book's vertical position in the air is
[tex]y=78.4\,\mathrm m-\dfrac12gt^2[/tex]
where [tex]g=9.80\,\frac{\mathrm m}{\mathrm s}[/tex]. It reaches the ground when [tex]y=0[/tex], at a time [tex]t[/tex] such that
[tex]0=78.4\,\mathrm m-\dfrac12gt^2\implies t=4.00\,\mathrm s[/tex]
So it takes the book 4 seconds to reach the bottom. The given initial velocity is irrelevant since it only has a horizontal component; vertically, the book is starting from rest.