Question

With what minimum speed must you toss a 200 g ball straight up to hit the 15-m-high roof of the gymnasium if you release the ball 1.1 m above the ground? Solve this problem using energy.

With what speed does the ball hit the ground?

Answer 1

h_f = final height reached = 15 m

h_i = initial height = 1.1 m

V_i = initial speed

V_f = final speed at height 15 m = 0 m/s

using conservation of energy

initial PE + initial KE = final PE + final KE

mgh_i + (0.5) m V_i² = mgh_f + (0.5) mV_f²

9.8 (1.1) + (0.5) V_i² = (9.8) (15) + (0.5) (0)²

V_i = 16.5 m/s

motion from height h = 1.1 m to h = 0 m at ground

V_b = speed at bottom

using conservation of energy

initial PE + initial KE = PE at ground + KE at ground

mgh_i + (0.5) m V_i² = mgh_f + (0.5) mV_b²

9.8 (1.1) + (0.5) (16.5)² = (9.8) (0) + (0.5) V_b²

V_b = 17.2 m/s