Newtons law of motion

Question

A body of mass m is projected with initial speed u at an angle owith the horizontal. The change in momentum of body after time t is

1. mu sino

2. 2 mu sino

3. mgt

4. zero

Answer 1

Momentum, p, is a vector quantity:

 

p = p_xi + p_yj

 

The initial value of the momentum is:

 

p(0) = (u·cos θ)i + (u·sin θ)j

 

The x-component has no force acting on it, so after time t it is still p_x = u·cos θ.  The y component is affected by the force of gravity on the body, F = mg, and after time t is given by p_y = u·sin θ + mgt.  Hence the momentum after time t is:

 

p(t) = (u·cos θ)i + (u·sin θ + mgt)j

 

The change in momentum is:

 

p(t) - p(0) = (u·cos θ - u·cos θ)i + (u·sin θ + mgt - u·sin θ)j = (mgt)j