Question

Romeo is throwing pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden h = 8.8 m below her window and L = 9.5 m from the base of the wall (Figure 1).

How fast are the pebbles going when they hit her window?

Answer 1

Let us consider the upwards direction as positive and the downwards direction as negative.

Gravitational acceleration = g = 9.81 m/s²

Initial velocity pebble = V₁

Initial horizontal velocity of the pebble = V_1x

Initial vertical velocity of the pebble = V_1y

Velocity of the pebble when it hits the window = V₂

The pebble hits the window with only a horizontal component.

Horizontal velocity of the pebble when it hits the window = V_2x = V₂

Vertical velocity of the pebble when it hits the window = V_2y = 0 m/s

Time taken to reach the window = T

V_2y = V_1y + gT

0 = V_1y + (-9.81)T

V_1y = 9.81T

Height of the window = H = 8.8 m

H = V_1yT + gT²/2

8.8 = (9.81T)T + (-9.81)T²/2

8.8 = 4.905T²

T = 1.34 sec

Horizontal distance covered by the pebble = L = 9.5 m

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

V_1x = V_2x

V_1x = V₂

L = V_1xT

9.5 = V₂(1.34)

V₂ = 7.09 m/s

Speed of the pebble when they hit the window = 7.09 m/s