Question

A 2.50-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

F = MA

F = 2.5 x 9.8

F = 24.5 N

Time needed to fall 

3.5 = 0.5 x 9.5 x t^2
t      = 0.845 s

Impulse  = F x t
= 24.5 x 0.845 

=20.7025

Answer 2

Answer:

The impulse is 21.41 kg-m/s.

Explanation:

Given that,

Mass of stone = 2.50 kg

Height = 3.75 m

We need to calculate the time

Using equation of motion

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

Where, s = height

u = initial speed

t = time

Put the value in the equation

$3.75=0+\dfrac{1}{2}\times9.8\times t^2$

$t^2=\dfrac{3.75\times2}{9.8}$

$t=\sqrt{\dfrac{3.75\times2}{9.8}}$

$t=0.874\ sec$

We need to calculate the impulse

Using formula of impulse

$J=F\times t$

$J=mg\times t$

Put the value into the formula

$J=2.50\times9.8\times0.874$

$J=21.41\ kg-m/s$

Hence, The impulse is 21.41 kg-m/s.