Question

An 85-kg runner is accelerating at a rate of 2 m/s^2 and a 65-kg runner at a rate of 3 m/s^2. If the heavier runner started at a speed of 1 m/s while the lighter runner started off stationary, then how long is it before the runners have the same momentum?

Answer 1

Answer

Mass of first runner m₁=85Kg

Initial velocity u₁=1$\frac{m}{sec}$

Accereation a₁=2 $\frac{m}{sec^2}$

For second runner

Mass m₂=65Kg

Initial velocity u₂=0(staionary)

Acceleration a₂=$3\frac{m}{sec}$

For given case momentum is same after t time velocities

For first runner

$v_1=u_1+at\\=1+2t$

Similiarly

$v_2=u_2+at\\=0+3t$

Now given is that momentum is same after t time.

$m_1v_1=m_2v_2\\$

$\frac{v_1}{v_2}=\frac{m_2}{m_1}=\frac{65}{85}$

Putting velocity value

$\frac{3t}{1+2t}=\frac{13}{17}$

Now solving this equation we get value of t=3.4 sec.