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)?
A) 10 m/s
B) 22 m/s
C) 44 m/s
D) 62 m/s
E) 120 m/s

Question

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)? 
A) 10 m/s 
B) 22 m/s 
C) 44 m/s 
D) 62 m/s 
E) 120 m/s

Quizplus · Accepted Answer

At point Q, the roller coaster has only potential energy which is given by mgh, where m is the mass of the roller coaster, g is the acceleration due to gravity and h is the height of the roller coaster from the ground. Let's assume that the roller coaster has mass m = 1000 kg. Then, h = 45 m - 25 m = 20 m (since we are starting from a height of 45 m and ending at a height of 25 m). Thus, the potential energy at point Q is:

PEQ = mgh = 1000 kg * 9.8 m/s^2 * 20 m = 196000 J

At point S, the roller coaster has both potential energy and kinetic energy. Let's assume that the roller coaster has a velocity v at point S. Then, the total energy at point S is given by:

PES = mgh + (1/2) * mv^2

Since energy is conserved, we can equate PEQ with PES:

PEQ = PES
196000 J = mgh + (1/2) * mv^2

Solving for v, we get:

v = sqrt(2gh) = sqrt(2 * 9.8 m/s^2 * 20 m) = 19.8 m/s

Therefore, the speed of the roller coaster at the top of the 25-m peak is approximately 20 m/s or 22 m/s (rounded to the nearest whole number). The best choice is B.

The Figure Shows a Famous Roller Coaster Ride