Question

Question #4a457

Answer 1

The velocity should be `-23m/s` as it hits the ground, with the time being either `1.8` seconds or `1.9` seconds depending on how you round.

Explanation:

Make a list of the terms you currently have, and the ones you need to solve for.

velocity(initial) = `-4.5m/s` (or 4.5m/s down)
distance = -25m (or 25m down)
acceleration = `-9.81m/s^2` (or 9.81m/s down)
velocity(final) = ? m/s
time = ? s

You can use the formula v(final)^2 = v(initial)^2 + 2ad to solve for the final velocity.

`v^2 = (-4.5m/s)^2 + 2(-9.81m/s)(-25m)`

`v^2 = 510m/s` (rounded to 2 significant figures)

`v = 22.6m/s` down

or `23m/s` down (rounded to 2 s.f.)

Now, on to the time. This can be solved using v(final) = v(initial) + at

Rearrange the equation so that we are solving for `t`;
`t =[v(f) - v(i)]/a`

v(final) = `-23m/s`; v(initial) = `-4.5m/s`; a = `-9.81m/s^2`

`t = (-23m/s--4.5m/s)/(-9.81m/s^2)`
`t = (-23m/s+4.5m/s)/(-9.81m/s^2)`
`t = (-18.5m/s)/(-9.81m/s^2)`
`t = 1.9s`

(Note: if you stored the exact values in your calculator for these steps, and didn't round to the 2 signature figures until the end, then your answer would have been 1.8 seconds.)

Hope this helps!

I'm currently learning about the exact same concepts at school, too.

Best wishes,
A fellow highschool physics student