Question

A ball, mass is 8 kg, is thrown from the top of a 30 m cliff with a velocity of 20 m/s straight up. The ball misses the cliff on the way down. Ignore air resistance. Use work and conservation of energy to find the following values.

a. what is the work done by gravity while the ball is in the air?

b. what is the maximum height of the ball?

c. what is the magnitude of the velocity just as the ball hits the ground?

d. would the energy in the system change if I threw the ball at an angle of 20 degrees?

Answer 1

here,

mass , m = 8 kg

h0 = 30 m

intial velocity , v0 = 20 m/s

a)

the work done by gravity while the ball is in the air , Wg = m * g * h0

Wg = 8 * 9.81 * 30 J

Wg = 2354.4 J

b)

let the maximum height of the ball be h

using conservation of energy

m *g * h0 + 0.5 * m* v0^2 = m * g * h

9.81 * 30 + 0.5 * 20^2 = 9.81 * h

solving for h

h = 50.4 m

the maximum height is 50.4 m

c)

let the magnitude of the velocity just as the ball hits the ground be v

using conservation of energy

maximum potential energy = maximum kinetic energy

m * g * h = 0.5 * m * v^2

9.81 * 50.4 = 0.5 * v^2

solving for v

v = 31.4 m/s

the magnitude of the velocity just as the ball hits the ground is 31.4 m/s

d)

No, the total energy of the system remains the same