.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

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

as,

s indicates height

u indicates initial speed

t indicates time

Now, we will use the equation and put the values

t = 0.874 seconds

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

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

J = 21.41 kg-m/s.

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s