Question

.50-kg stone is dropped from rest at a height of 3.75 m. What impulse does gravity impart to this stone from the instant it is dropped until it hits the ground, assuming negligible air resistance

Answer 1

Answer:

21.41 kg-m/s.

Explanation:

Data provided

Height = 3.75 m

Mass of stone = 2.50 kg

The computation of impulse is shown below:-

First we will compute the time using motion's equation  which is

$s = ut + \frac{1}{2} gt^2$

as,

s indicates height

u indicates initial speed

t indicates time

Now, we will use the equation and put the values

$3.75 = 0 + \frac{1}{2}\times 9.8\times t^2\\\\t^2 = \frac{3.75\times 2}{9.8}\\\\t= \sqrt{\frac{3.75\times 2}{9.8} }$

t = 0.874 seconds

After computing the time now we will find put the impulse  which is

$J = F\times t\\\\J = mg\times t$

Now we will put the values into the above formula to reach the impulse

$J = 2.50\times 9.8\times 0.874$

J = 21.41 kg-m/s.