Question

A cannonball is fired from a cliff top horizontally out to sea with a speed of 74m/s. The cliff is 320m above sea level. Calculate the speed of impact?

how do you calculate the speed of impact pls help!!

Answer 1

`"speed of impact" = 108 m/s`

Explanation:

The question does not say anything about air resistance, so we are to ignore air resistance. This simplifies the problem significantly.

Therefore the cannonball's horizontal velocity, `v_h`, continues without change. It gains velocity in the vertical direction according to the suvat formula

`v^2 = u^2 + 2*a*s " "` where

• u = 0 because the cannonball is fired horizontally
• `a = 9.8 m/s^2`
• and s = 320 m.

Filling the data into that formula will give us the final vertical velocity, `v_v`.

`v_v^2 = 0^2 + 2*9.8 m/s^2*320 m = 6272 m^2/s^2`
`v_v = sqrt(6272 m^2/s^2) = 79.2 m/s`

The cannonball's speed of impact is the magnitude of its final velocity. The final velocity will be the vector sum of its `v_h` and `v_v`.

`"speed of impact" = sqrt(v_h^2 + v_v^2)`
`"speed of impact" = sqrt((74m/s)^2 + (79.2 m/s)^2)`
`"speed of impact" = sqrt(11,748 m^2/s^2) = 108 m/s`

I hope this helps,
Steve