Question

A spherical ball of mass 20kg is stationary at the top of a hill of height 100m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30m, and finally rolls down to a horizontal base at a height of 20m above the ground. What is the velocity attained by the ball?

a) 10m/s
b) 15m/s
c) 20m/s
d) 25m/s

Answer 1

To find the velocity attained by the ball, we need to consider the conservation of mechanical energy. The velocity at the bottom of the first hill is approximately 20 m/s.

Step-by-step explanation:

To find the velocity attained by the ball, we need to consider the conservation of mechanical energy. As the ball rolls down the first hill, it gains kinetic energy from its potential energy at the top. The potential energy is given by the equation PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the hill.

Let's calculate the potential energy at the top of the first hill:

PE = (20 kg)(9.8 m/s^2)(100 m) = 19600 J

Since kinetic energy is given by the equation KE = 1/2 mv^2, we can calculate the velocity at the bottom of the first hill:

KE = 19600 J = 1/2 (20 kg) v^2

Solving for v, we find that the velocity at the bottom of the first hill is approximately 20 m/s.

Therefore, the correct answer is c) 20m/s.