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 = 9.1 m below her window and L = 7.3 m from the base of the wall. How fast are the pebbles going when they hit her window? Express your answer to two significant figures and include the appropriate units.

Answer 1

This is a case of projectile motion as Romeo needs to throw the pebble with an initial velocity 'u' making some angle (θ<90°) with the horizontal to hit Juliet's window (as he stands some distance (7.3 m, given) away from the base of the wall)

We know, that a projectile has a non-zero horizontal component of velocity along with a zero vertical component of velocity at its maximum height. As mentioned in the question, Romeo wants the pebbles to hit the window with only the horizontal component of velocity, the maximum height of the projectile is equal to the height of the window from the base of the wall.

So, the following information is given :

Maximum height of the projectile, H = 9.1 m

Now, formula for maximum height of a projectile is given by,

H = {(u^2)×(sin θ​) ^2} / (2 × g)

Where, u sin θ is the vertical component of velocity

Substituting given value of 'H' and g=9.8 m/sq. s in the formula, we get,

9.1 = {(u^2)×(sin ​θ​) ^2} / (2× 9.8)

Which gives us, u sin θ = sqrt (H × 2 × g)

= Sqrt ( 9.1 × 2 × 9.8)

= 13.355 m/s

Formula for time of maximum height, tm= ( u sin θ) / g

Substituting the value of 'u sin θ' and g in the above formula, we get,

tm = 13.355 / 9.8

= 1.36 s

The pebbles are taking a time equals to 1.36 s to hit the window.