Question

A soccer ball is kicked from the top of one building with a height of H1 = 30.3 m to another building with a height of H2 = 13.4 m. The ball is kicked with a speed of v0 = 15.1 m/s at an angle of θ = 80.0° with respect to the horizontal. The mass of a size 5 soccer ball is m = 450 g. What is the speed of the soccer ball, when it lands on the roof of the second bulding? The soccer ball is kicked without a spin. Neglect air resistance.

Answer 1

As the ball moves under the effect of gravitational force only, which is a conservative force, total mecahnical energy of ball remains constant.

Sum of kinetic and potential energies of ball when kicked is equL to sum of sum of these energies on landing the other roof.

Hence gain in kinetic energy is equal to loss in potential energy.

Let speed of ball on landing on the roof is v

m = mass of ball

m(v²-v₀²)/2 = mg(h₁-h₂)

v²= 2g(h₁-h₂) + v₀²

v²= 2 ×9.8×(30.3-13.4) + (15.1)²= 559.25 m²s^-2

v= 23.65 ms^-1