Question

Use the impulse-momentum theorem to find how long a stone falling straight down takes to increase its speed from 3.7 m/s to 9.30 m/s . Express your answer using two significant figures.

Answer 1

Answer:

0.57 s

Explanation:

We are given that

Initial velocity of stone=$v_i=3.7m/s$

Final velocity of stone=$v_f=9.3m/s$

We have to find the time taken by stone to increases its speed from 3.7m/s to 9.3 m/s.

We know that

From Impulse momentum theorem

$Impulse=$Change in momentum

$F_{avg}\Delta t=mv_f-mv_i=m(v_f-v_i)$

Stone falls freely therefore $F_{avg}=F_g$=mg

$mg\Delta t=m(9.3-3.7)$

$g\Delta t=5.6$

$g=9.8m/s^2$

Using the value of g

$\Delta t=\frac{5.6}{9.8}=0.57 s$

Hence, the stone takes 0.57 s to increase its speed from 3.7 m/s to 9.3 m/s.