Question

Two ice skaters, one with a mass of 45 kg and the other with a mass of 60 kg, push off against one another starting from a stationary position. After they have pushed off, the relative speed at which they separate is 0.600m/s. What is the speed of the 60kg skater?

Answer 1

Answer:

0.25714 m/s

Explanation:

$m_1$ = Mass of 45 kg skater

$m_2$ = Mass of 60 kg skater

$v_1$ = Speed of 45 kg skater

$v_2$ = Speed of 60 kg skater

As the momentum is conserved

$m_1v_1+m_2v_2=0\\\Rightarrow 45v_1+60v_2=0\\\Rightarrow v_1=-\frac{60v_2}{45}\\\Rightarrow v_1=-\frac{4}{3}v_2$

$v_r$ = Relative speed = 0.6 m/s

$v_r=v_2-v_1\\\Rightarrow v_r=v_2-\left(-\frac{4}{3}v_2\right)\\\Rightarrow 0.6=\frac{7}{3}v_2\\\Rightarrow v_2=\frac{0.6\times 3}{7}\\\Rightarrow v_2=0.25714$

The speed of the 60kg skater is 0.25714 m/s