Question

A 64.6-kg boy and a 49.1-kg girl, both wearing skates face each other at rest on a skating rink. The boy pushes the girl, sending her eastward with a speed of 3.57 m/s. Determine the subsequent speed (in m/s) of the boy.
a. 2.7 m/s
b. 4.7 m/s
c. 31.8 m/s

Answer 1

Answer:

a. 2.7 m/s

Explanation:

Total momentum must be conserved before and after the push. Since they were both at rest before, their total speed, and momentum, is 0, so is the total momentum after the push

$m_bv_b + m_gv_g = 0$

where $m_b = 64.6, m_g = 49.1$ are the mass of the boy and girl, respectively. $v_g = 3.57 m/s, v_b$ are the velocities of the girl and boy after the push, respectively. We can solve for $v_b$

$64.6v_b + 49.1*3.57 = 0$

$v_b = -49.1*3.57/64.6 = -2.71 m/s$

So the boy speed is 2.7 m/s after pushing the girl