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 = (5)/(9.8)`

`t = 0.51s`

Therefore it will take 0.51s.