Question

A ball weighing 200 g is thrown vertically upwards with a speed of 20 m/s. what will be its momentum at the highest point?
(A) Zero
(B) 4 \[kgm/s\]
(C) 4000 \[kgm/s\]
(D) None of these

Answer 1

Hint: At highest point the velocity of any object, irrespective of mass, thrown vertically upward is equal to zero. The momentum of a particle is the product of its velocity and its momentum.
Formula used:
 In this solution we will be using the following formulae;
\[p = mv\] where \[p\] is the momentum of a particle, \[m\] is the mass of the particle or object, and \[v\] is the velocity of the object.

Complete Step-by-Step Solution:
A ball of a particular mass is said to be thrown vertically upwards with a particular speed. We are to find the momentum at its maximum height.
In general, when a body is thrown vertically upwards (i.e. no horizontal component of velocity) at a particular initial velocity, gravitational force acts downward on the body the moment the body leaves the hand or the machine which projected it. Since, the gravity acts downward, and the velocity is upward, it tends to reduce the upward velocity of the object (or increase the downward velocity) until the object attains a maximum height. This height is the point where the object has “no velocity left” to move further, hence starts to accelerate downward due to the acceleration due to gravity acting downwards. Hence at maximum height, the velocity of an object is zero.
And since momentum can be defined as
\[p = mv\] where \[m\] is the mass of the particle or object, and \[v\] is the velocity of the object, we have that
\[p = 200\left( 0 \right) = 0\]

Hence, the correct option is A.

Note: Although, for a vertically thrown projectile, the momentum at maximum height is zero, for a projectile thrown at an angle (less than 90 degrees) to the horizontal, the horizontal component of the velocity will still exist, and thus will have momentum, even though the vertical component will still be zero.