Answer to Question #256972 in Mechanics | Relativity for Joey

Question

A 0.5Kg rider travelling to the right at 2ms-1 collides with a stationary rider of mass 1Kg. Find the velocities of the two riders after the collision if: a. It is perfectly elastic.

Answer 1

$m_1 = 0.5kg; v_1=2\frac{m}{s}$

$m_2 = 1kg;v_2=0$

$\text{Since a perfectly elastic collision:}$ $\text{}$

$m_1v_1+m_2v_2 = m_1u_1+m_2u_2\ (1)$

$\frac{m_1v_1^2}{2}+\frac{m_2v_2^2}{2}=\frac{m_1u_1^2}{2}+\frac{m_2u_2^2}{2}\ (2)$

$\text{from }(1)$

$0.5*2+1*0= 0.5u_1+1*u_2$

$u_2= 1-0.5u_1\ (3)$

$\text{from }(2)$

$\frac{0.5*2^2}{2}+\frac{1*0^2}{2}=\frac{0.5*u_1^2}{2}+\frac{1*u_2^2}{2}$

$u_2^2 = 2-0.5u_1^2\ (4)$

$\text{from (3) and (4)}$

$u_2^2>0$

$2-0.5u_1^2>0$

$u_1^2<4$

$(1-0.5u_1)^2=2-0.5u_1^2$

$0.75u_1^2-u_1-1 =0$

$u_1\approx -0.67\frac{m}{s}$

$u_1'=2(\text{does not satisfy the condition }u_1^2<4)$

$u_2= 1-0.5u_1= 1+0.5*0.67\approx 1.34\frac{m}{s}$

$\text{Answer:}$

$-0.67\frac{m}{s}\text{ first rider speed after collision}$

$1.34\frac{m}{s}\text{ second rider speed after collision}$