Hello Jessie.

Since there is no horizontal acceleration, the horizontal component of velocity when the pebble strikes the window is the same as the horizontal component of velocity when it leaves Romeo's hand, let's call that v_h.

To find this constant horizontal velocity, we need the horizontal distance (given) and the time between the pebble leaving Romeo's hand and the window strike.

We know that the vertical speed of the pebble when it hits the window must be zero because he is going to throw the pebble such that it has only a horizontal component of velocity when it strikes the window.

This means that the time it takes gravity to slow the vertical component of velocity to zero is the same time as it takes to move horizontally from Romeo's hand to the window.

The formula that relates two velocities, one distance and one acceleration together for constant linearly accelerated objects is one you should have encountered already:

v² = v₀ ² + 2ad_v

Once you have this vertical component of initial velocity, you can use it to find the time by using this formula:

v= v₀ + at

This value t is the time you need to use to find the constant horizonal velocity using the fundamental formula:

d_h = v_h t

where d_h represents the horizontal displacement and v_h represents the horizontal velocity you want to find.

Hope this helps,
Stephen La Rocque.