Question

At point 2, the roller coaster is clocked moving at 46 m/s. How fast is it moving at point 4? Given that h1 = 40 m, h2 = 20 m, and h3 = 35 m. (Note: h2 corresponds to the height at position 4, not 2). What is the speed at point 4?

A) 34 m/s
B) 46 m/s
C) 52 m/s
D) 58 m/s

Answer 1

To find the speed at point 4 of the roller coaster, we can use the principle of conservation of energy and the equation for kinetic energy.

Step-by-step explanation:

To find the speed at point 4 of the roller coaster, we can use the principle of conservation of energy. The potential energy at point 2 is converted into kinetic energy at point 4. Given that h2 = 20 m and h3 = 35 m, we can calculate the change in potential energy between points 2 and 4:

ΔPE = mgh = mg(h3 - h2)

Next, we can equate the change in potential energy to the change in kinetic energy:

ΔPE = ΔKE

Finally, we can solve for the speed at point 4 using the equation for kinetic energy:

KE = 1/2mv^2

By substituting the known values and solving for v, we can find the speed at point 4.