Romeo is chucking 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 4.5 m below her window and 5.0 m from the base of the wall (Fig. 3-34). How fast are the pebbles going when they hit her window?

The speed at which the pebbles are going when they hit the window is gotten as;

v_h = 5.21 m/s

We are given;

Vertical displacement; h = 4.5 m

Horizontal displacement; d = 5 m

Now, know the pebbles are thrown such that they have only a horizontal component of velocity when they strike the window. Thus, the final vertical component(v) of the velocity of the pebble when it hits the window must be equal to zero.

Thus; v = 0 m/s

Let's Calculate the initial vertical component of the velocity from;

v² = u² + 2gh

0 = u² + 2(-9.8 × 4.5)

u² = 88.2

u = √(88.2)

u = 9.3915 m/s

Now, let us find the time from;

v = u + gt

0 = 9.3915 - 9.8t

t = 9.3915/9.8

t = 0.9583 s

Thus, speed at which the pebbles are going when they hit the window is;

v_h = d/t

v_h = 5/0.9589

v_h = 5.21 m/s

Read more at; link

Explanation:

Given the following :

Horizontal distance = distance from base of the wall = 5m

Vertical distance = - 4.5m

Acceleration due to gravity g = 0 (horizontal motion) g = 9.8m/s² (vertical motion)

To obtain time :

From S = 0.5 at²

-4.5 = 0.5 × 9.8 × t²

-4. 5 = 4.9t²

-4.5 / 4.9 = t²

- 0.9183673 = t²

t = 0.9583148

Hence, horizontal Velocity = distance / time

Vx = 5 / 0.9583148

= 5.2174919 m/s