Question

A small sphere of mass 2 kg moving with velocity 4i -7j m/s collides with a smooth wall and returns with a velocity -i +3j m/s the magnitude of impulse received by the ball

Answer 1

here, we have to use formula,
impulse = change in momentum
impulse = Pf - Pi
impulse = m(Vf - Vi)

here, m = 2 kg
Vf = (-i + 3j ) m/s
Vi = (4i - 7j) m/s

now,
impulse = 2 × ( -i + 3j - 4i + 7j)
= 2 × ( -5i + 10j)
=(-10i + 20j ) kg.m/s

hence, magnitude of impulse = √(10²+20²)
= 10√5 N.s

Answer 2

here, we have to use formula,

impulse = change in momentum

impulse = Pf - Pi

impulse = m(Vf - Vi)

here, m = 2 kg

Vf = (-i + 3j ) m/s

Vi = (4i - 7j) m/s

now,

impulse = 2 × ( -i + 3j - 4i + 7j)

= 2 × ( -5i + 10j)

=(-10i + 20j ) kg.m/s

hence, magnitude of impulse = √(10²+20²)

= 10√5 N.s^(-1)