Question

A toy car is traveling down a small ramp. While it is at a height of 0.4 m, it is traveling down the ramp at 2.2 m/s (ignore friction and air resistance, and assume that the bottom of the ramp has a height of 0 m).

What is the speed of the car when it reaches the bottom of the ramp? (Correct answer: about 3.5 m/s.)

a) 3.0 m/s
b) 3.5 m/s
c) 4.0 m/s
d) 2.0 m/s

Answer 1

To find the speed of the car at the bottom of the ramp, we can use the principle of conservation of mechanical energy. The speed of the car when it reaches the bottom of the ramp is approximately 3.5 m/s.

Step-by-step explanation:

To find the speed of the car at the bottom of the ramp, we can use the principle of conservation of mechanical energy. The initial potential energy of the car at the top of the ramp is equal to its final kinetic energy at the bottom of the ramp.

At the top of the ramp, the car has a potential energy of mgh, where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the ramp. At the bottom of the ramp, the car has a kinetic energy of (1/2)mv^2, where v is the speed of the car. Since there is no friction or air resistance, the total mechanical energy of the car is conserved.

Using the conservation of energy, we can set the initial potential energy equal to the final kinetic energy:

mgh = (1/2)mv^2

Canceling out the mass:

gh = (1/2)v^2

Solving for v:

v = sqrt(2gh)

Plugging in the values given in the question (g = 9.8 m/s^2 and h = 0.4 m):

v = sqrt(2 * 9.8 * 0.4) ≈ 3.5 m/s.