Question

Two space ships collide in deep space. Spaceship P, the projectile, has a mass of 4M,

while the target spaceship T has a mass of M. Spaceship T is initially at rest and the
collision is elastic. If the final velocity of Tis 8.1 m/s, what was the initial velocity of
P?

Answer 1

The initial velocity of spaceship P was u₁ = 5.06 m/s

Step-by-step explanation:

In an elastic collision between two bodies the expression for the final velocity of the second body is given as follows:

`V_(2) = ((m_(2)-m_(1)) )/((m_(1)+m_(2)))u_(2) + (2m_(1) )/((m_(1)+m_(2)))u_(1)`

Here, subscript 1 is used for spaceship P and subscript 2 is used for spaceship T. In this equation:

V₂ = Final Speed of Spaceship T = 8.1 m/s

m₁ = mass of spaceship P = 4 M

m₂ = mass of spaceship T = M

u₁ = Initial Speed of Spaceship P = ?

u₂ = Initial Speed of Spaceship T = 0 m/s

Using these values in the given equation, we get:

`8.1 m/s = (M-4M )/(4M+M)(0 m/s) + (2(4M) )/(4M+M)u_(1)`

8.1 m/s = (8 M/5 M)u₁

u₁ = (5/8)(8.1 m/s)

u₁ = 5.06 m/s