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?

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

Explanation:

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

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 = (8 M/5 M)u₁

u₁ = (5/8)(8.1 m/s)

u₁ = 5.06 m/s

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.