Question

a ball is thrown up at an angle 45° with the horizontal then the total change of momentum by the instant it returns to ground is:-

Answer 1

let a ball of mass m is projected upward with speed v inclined with horizontal 45° .
initial velocity( U) = vcos∅i + vsin∅ j

at t time velocity of objects (V) =
vcos∅i + ( vsin∅ -gt) j

if t = time of flight then body return to ground and it's velocity then
( V) = vcos∅ i +( usin∅ -g2usin∅/g)j
=vcos∅ i - vsin∅ j

now ,

change in momentum = final momentum - initial momentum

= m( vcos∅i -vsin∅ j -vcos∅i -vsin∅j )

= -2mvsin∅ j
here ∅ = 45°

then ,
change in momentum = -√2mv j

Answer 2

Answer:

hope it helps u

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