The figure shows a famous roller coaster ride.You can ignore friction.If the roller coaster leaves point Q from rest,what is its speed at the top of the 25-m peak (point S)?

Question

Quizplus · Accepted Answer

At point Q, the roller coaster has potential energy (mgh), where m is the mass of the roller coaster, g is the acceleration due to gravity, and h is the height of point Q above the ground. When the roller coaster reaches the top of point S, all of its potential energy has been converted to kinetic energy (1/2 mv^2), where v is the speed of the roller coaster. Therefore, we can use the conservation of energy to solve for v:

mgh = 1/2 mv^2

Canceling the mass and multiplying both sides by 2, we get:

2gh = v^2

Plugging in the values, we get:

2(9.8 m/s^2)(25 m) = v^2

Simplifying, we get:

v = 22.14 m/s

So, the speed of the roller coaster at the top of point S is approximately 22 m/s, which is closest to choice B.

The Figure Shows a Famous Roller Coaster Ride