Question

A 83.5-kg boy and a 63.6-kg girl, both wearing skates face each other at rest on a skating rink. The boy pushes the girl, sending her to the left with a velocity of -3.11 m/S. A

Neglecting friction, determine the subsequent velocity of the boy to the right.
Answer: +____m/s

Answer 1

i.e. velocity of boy is 2.82 m/s towards west

Step-by-step explanation:

Given

mass of boy m_b=70.9\ kgm

b

=70.9 kg

mass of girl m_g=43.2\ kgm

g

=43.2 kg

speed of girl after push v_g=4.64\ m/sv

g

=4.64 m/s

Suppose speed of boy after push is v_bv

b

initially momentum of system is zero so final momentum is also zero because momentum is conserved

P_i=P=fP

i

=P=f

0=m_b\cdot v_b+m_g\cdot v_g0=m

b

⋅v

b

+m

g

⋅v

g

v_b=-\frac{m_g}{m_b}\times v_gv

b

=−

m

b

m

g

×v

g

v_b=-\frac{43.2}{70.9}\times 4.64v

b

=−

70.9

43.2

×4.64

v_b=-2.82\ m/sv

b

=−2.82 m/s

i.e. velocity of boy is 2.82 m/s towards west