A Hot Wheels car is moving at 2.7 m/s at the bottom of a 30degree incline. A stu

Question

A Hot Wheels car is moving at 2.7 m/s at the bottom of a 30degree incline. A student predicts that the car will travel a maximum distance of 92 cm along the incline. Is this a reasonable prediction? Explain fully. Make a graph on a separate sheet of paper of distance along the incline vs. speed at the bottom of the incline for cars starting up a fixed incline at various speeds? Explain in detail how you arrived at your graph. Ignoring friction, how would the angle of the incline affect how high above the base of the incline the car will ultimately travel? In other words, suppose a Hot Wheels car approaches two inclines, one at 20degree and one at 40degree. How will the maximum height above the base compare for the two inclines? Explain your reasoning fully.

Explanation / Answer

I am using conservation of energy to solve this problem. Assuming that there is no energy lost to friction or air resistance, the kinetic energy at the bottom is equal to the potential energy when it stops on the ramp because you haven't added or subtracted any energy from the system.

Kinetic energy = 0.5 x mass x velocity ^2
Potential energy = mass x height x gravity

So
0.5 x mass x v^2 = mass x height x gravity
Mass cancels and you know velocity and gravity, so you can solve for height:
0.5 x 2.7^2 = H x 9.81
H = 0.372 meters

Now you know the vertical height and the angle of the ramp so you can solve for total distance (hypotenuse of the triangle) with basic trig. Sine = opposite leg/hypotenuse

Sine (30) = height/hyp
hypotenuse = 0.372/ sin (30) = 0.742 meters

So the student in the example is wrong, it will travel 74.2 cm along the incline. Note that the actual result would be less due to friction and wind resistance.

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