Question

A toy rocket is shot straight up into the air with an initial velocity of 45 m/s. How long does it take the rocket to reach its highest point?

Answer 1

You will need the standard formulation for gravitational motion. It's a quadratic that looks like this: \(h(t) = 4.9t^{2} + V_{0}t + h_{0}\) -- Look familiar?

Answer 2

Every second from its initial motion,
the acceleration of gravity removes 9.81 m/s
from the toy rocket's initial speed
which means that in a time interval of
45.0/9.81 = 4.59 s <= ANS a.
the rocket's speed = 0 {at max height}

The average speed during this time = 45.0/2 = 22.5 m/s {constant accelerated motion}
The distance = max height = avg speed x time = (22.5)(4.59) = 103 m ANS b.