To determine the velocity with which the ball hits the ground, we can use the equations of motion. In this scenario, we assume there is no air resistance.
The initial velocity (u) of the ball when thrown vertically upward is +10 m/s because the upward direction is considered positive. The acceleration due to gravity (g) is approximately 9.8 m/s², acting downward. The displacement (s) of the ball is -75 m since it moves upward initially.
We can use the following equation of motion to calculate the final velocity (v) of the ball when it hits the ground:
v² = u² + 2as
Plugging in the known values:
v² = (+10 m/s)² + 2(-9.8 m/s²)(-75 m)
v² = 100 m²/s² + 1470 m²/s²
v² = 1570 m²/s²
Taking the square root of both sides:
v ≈ √(1570 m²/s²)
v ≈ 39.6 m/s
Therefore, the velocity with which the ball hits the ground is approximately 39.6 m/s.