Question

A ball thrown horizontally with speed vi = 30.0 m/s travels a horizontal distance of d = 57.0 m before hitting the ground. From what height h was the ball thrown?

Answer 1

Let us consider the upward direction as positive and the downward direction as negative.

Gravitational acceleration = g = -9.81 m/s²

Initial velocity of the ball = V₀ = 30 m/s

The ball is thrown horizontally.

Initial horizontal velocity of the ball = V_x0 = 30 m/s

Initial vertical velocity of the ball = V_y0 = 0 m/s

Initial height of the ball = h

Horizontal distance traveled by the ball before hitting the ground = d = 57 m

Time taken by the ball to hit the ground = T

There is no horizontal force acting on the ball therefore the horizontal velocity of the ball remains constant.

d = V_x0T

57 = (30)T

T = 1.9 sec

The displacement of the ball in the vertical direction is downwards when the ball hits the ground therefore it is negative.

-h = V_y0T + gT²/2

-h = (0)(1.9) + (-9.81)(1.9)²/2

h = 17.71 m

Height from which the ball was thrown = 17.71 m