Question

a model rocket rises with constant acceleration to a height of 3.3m, at which this point its speed is 28.0 m/s . How much time does it take to reach this height?

Answer 1

A model rocket rises with constant acceleration to a height of $3.3\mathrm{m}$, at which this point its speed is 28.0 m/s. How much time does it take to reach this height?

Assuming that initial speed is 0 we can write an equation for body, which moving with constant acceleration:

$$h = \frac{a t^{2}}{2}$$

We know rocket speed at this height, so we can wind acceleration:

$$a = \frac{v}{t}$$ $$h = \frac{v t^{2}}{2 t} = \frac{v t}{2} \rightarrow t = \frac{2 h}{v}$$ $$t = \frac{2 * 3.3 \, \mathrm{m}}{28 \, \mathrm{m/s}} \cong 0.24 \, \mathrm{s}$$

Answer: $t \cong 0.24 \, \mathrm{s}$