Question

Use the impulse-momentum theorem to find how long a stone falling straight down takes to increase its speed from 5.6 m/s to 10.6 m/s . Express your answer in seconds.

Answer 1

As stated, the impulse and momentum definitions will be used to later find the value of time through the force of gravity. According to the theory, the impulse formula is given as,

$I = F\Delta t$

Here,

F = Force

$\Delta t =$ Change in time

Now using the impulse theorem we have that,

Change in Impulse = Change in momentum

$F\Delta t = \Delta p$ (1)

The change in momentum is given as

$\Delta p = p_f -p_i$

$\Delta p = (-10.6)-(-5.6)$

$\Delta p = -5m/s$

The force due to gravity is through the Newton's second law

$F_g = -mg$

Here,

m = mass

g = Acceleration due to gravity

Substitute the value in (1)

$-mgt = -5m/s$

$9.8t = 4.9$

$t = \frac{5}{9.8}$

$t = 0.51s$

Therefore it will take 0.51s.