How to solve... A projectile is fired on top of a cliff 92m high

Question

A projectile is fired on top of a cliff 92m high with a velocity of 430m/s directed 45° with the horizontal. Find the range on a horizontal plane from the base of the cliff.

Answer: 18, 958m

Answer 1

First consider the vertical direction.

In the vertical direction, we're given: change in height, initial velocity, and acceleration.

We can find the time

Change in height = -92m (negative since it's falling)

Initial velocity = 430sin(45). (This is the y-component of the velocity)

Acceleration = -9.8m/s²

We can use the equation to solve for time: Δheight = 1/2at²+v₀t

Once you get t, we can consider the horizontal direction

Use the equation x = vt

v = 430cos(45) and t is the same as before.