Question

Two gliders move toward each other on a linear air track, which we assume is frictionless. Glider A has a mass of 0.50 kg, and glider B has a mass of 0.30 kg; both gliders move with an initial speed of 2.0 m/s. After they collide, glider B moves away with a final velocity whose x component is +2.0 m/s. What is the final velocity of A? Suppose glider B is initially moving to the left at 5.0 m/s when it runs into glider A, which is initially at rest. At what speed does glider A move away from the collision if glider B bounces back with a speed of 0.92 m/s?

Answer 1

Answer:

-0.4 m/s

-3.552 m/s

Explanation:

$m_1$ = Mass of first glider = 0.5 kg

$m_2$ = Mass of second glider = 0.3 kg

$u_1$ = Initial Velocity of first glider = 2 m/s

$u_2$ = Initial Velocity of second glider = -2 m/s

$v_1$ = Final Velocity of first glider

$v_2$ = Final Velocity of second glider = 2 m/s

As the linear momentum of the system is conserved we have

$m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_1=\dfrac{m_1u_1+m_2u_2-m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{0.5\times 2+0.3\times (-2)-0.3\times 2}{0.5}\\\Rightarrow v_1=-0.4\ m/s$

The velocity of glider A is -0.4 m/s

$u_1$ = 0

$u_2$ = -5 m/s

$v_2$ = 0.92 m/s

$m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_1=\dfrac{m_1u_1+m_2u_2-m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{0.5\times 0+0.3\times (-5)-0.3\times 0.92}{0.5}\\\Rightarrow v_1=-3.552\ m/s$

The velocity of glider A is -3.552 m/s