Problems -
Permutations
1. A person sitting in an open car moving at
constant velocity throws a ball vertically up into air. Where will the Ball
fall?
Solution:
Since the velocity is
constant, the horizontal component of velocity for the car and the ball are
same.
They cover equal
horizontal distances in the same time travel.
Therefore the ball will
Land in the hands of the person in the car.
2. A man is Standing Stationarily with respect to
a horizontal conveyor belt that is accelerating with 1 m 
as shown in Figure. What is the net force on
the man? If the coefficient of Static friction between the man’s shoes and the
belt is 0.2, upto what acceleration of the belt can the man continue to be stationary
relative to the belt? (Mass of the man = 65 kg).
Solution:
Mass
of the man,
= 65 Kg
Acceleration
of the belt, 
=
1 m
Coefficient
of Static friction, 
The
net force F, acting on the mass is given by Newton’s second law of motion as:
= 65 ×
1
= 65 N
The man will be continue to
be stationary with respect to the
conveyor belt unit the net force on the man is less than or equal to the Frictional
Force 
Exerted by the belt, i.e. ,
m
Therefore, the maximum
acceleration of the belt up to which the man can stand stationarily is 2 m
3. A Stream of water flowing Horizontally
with a speed of 
gushes out of a tube of cross-sectional area
,
and hits a vertical wall nearby . What is the force
exerted on the wall by the impact of water, Assuming it does not rebound?
Solution:
Speed of water scream,
Cross – sectional area of the
tube,
Volume of water coming out
from the pipe per second,
× 
Density of water,
Mass of water flowing out
through the pipe per second,
×
s
The water Strikes the wall and
does not rebound, therefore the force exerted by the water on the ball is given
by Newton’s second law of motion as:
Rate
of change of momentum
150
×
15
N