Question

A car of mass 2100 kg collides with a motorcycle of mass 290 kg. After the collision, the car and motorcycle stick and slide together. The car's velocity just before the collision was<30,-10>m/s , and that of the motorcycle was <10,10>m/s. Determine the velocity of the stuck-together car and motorcycle just after the collision.

Answer 1

Answer:

V = 29.49 m/s

Explanation:

Given that,

The mass of a car,$m_c=2100\ kg$

The mass of a motorcycle, $m_m=290\ kg$

The initial velocity of the car,$v_c=30i-10j$

$|v_c|=\sqrt{30^2+(-10)^2} =31.62\ m/s$

The initial velocity of the motorcycle,$v_m=10i+10j$

$|v_m|=\sqrt{10^2+10^2} =14.14\ m/s$

As they stick together. Let V is the speed. So, using the conservation of momentum,

$m_cv_c+m_mv_m=(m_c+m_m)V\\\\V=\dfrac{m_cv_c+m_mv_m}{(m_c+m_m)}\\\\V=\dfrac{2100\times 31.62+290\times 14.14}{(2100+290)}\\\\V=29.49\ m/s$

So, the velocity of the stuck together car and the motorcycle after the collision is 29.49 m/s.