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 = 8.1 m below her window and L = 7.4 m from the base of the wall (Figure 1).

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

Answer 1

Given that Romeo wants the pebbles to hit the window with only a horizontal component of velocity.

So when the pebbles hit the window, the vertical component of velocity is zero.

In projectile motion, at maximum height vertical component of velocity becomes zero

So the height of the window is equal to the maximum height of the projectile

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First, find the time taken by the pebble to strike the window

Consider the vertical motion of the projectile

Use formula

Pebble is going up and g is acting downwards, so put a negative sign for g

At the max height, vertical velocity becomes zero.

--------(1)

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Use formula

Pebble is going up and g is acting downwards, so put a negative sign for g

Put (1) in the above equation

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Consider the horizontal motion of the pebble

There is no acceleration in horizontal direction, so horizontal velocity remains constant.

Horizontal velocity = Horizontal distance/Time

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

ANSWER:

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