Question

A particle moving at 10 m/s along the x-axis collides elastically with another particle moving at 5.0 m/s in the same direction along the x-axis. the particles have equal masses. what are their speeds after the collision? Can someone please explain this in the simplest way possible?

Answer 1

Explanation:

It is given that,

Velocity of particle 1, u₁ = 10 m/s

Velocity of particle 2, u₂ = 5 m/s

Let v₁ and v₂ are the final speed of both particles after the collision. Applying the conservation of momentum as :

$mu_1+mu_2=mv_1+mv_2$

$15=v_1+v_2$......................(1)

For an elastic collision, the coefficient of restitution is equal to 1 as :

$\dfrac{v_2-v_1}{u_1-u_2}=1$

$\dfrac{v_2-v_1}{5}=1$

${v_2-v_1}=5$................(2)

On solving equation (1) and (2), we get,

$v_1=5\ m/s$

$v_2=10\ m/s$

So, the speeds of particle 1 and particle 2 after the collision is 5 m/s and 10 m/s respectively. Hence, this is the required solution.