Question

What is the speed and mass of the object?

The recoil of a projectile launcher finds that the linear momentum of an ejected object is 26.1 kg m/s, and the target is equipped with an energy detector that determines that the object has a kinetic energy of 200 J.

Answer 1

speed = 15.3256705`m/s`
mass = 1.703025 `kg`

Explanation:

From the Kinetic Energy and momentum formulas
`K.E=1/2*m*v^2`

and momentum
`P=mv`

we can get
`K.E = 1/2*P*v`

and we can get
`K.E = P^2/(2m)`
because `v=P/m`

so

for the speed, I will use `K.E = 1/2*P*v`

`200J = 1/2*26.1kg m/s*v`
`V = (200J)/((26.1kgm/s)*1/2) = 15.3256705 m/s`

for the mass, I will use `K.E = P^2/(2m)`
`m = P^2/(2K.E)`
`m = (26.1^2kgm/s)/(2*200J)` = 1.703025kg

Answer 2

`m = 1.70 kg`

`v = 15.32 m/s` away from the launcher.

By solving a system of equations.

Explanation:

We know the following based on the equations for momentum and kinetic energy.

`m*v = 26.1 (kg m)/s` (this is equation1)

`1/2 m*v^2 = 200J` (this is equation2)

To solve the above system of equations, we need to isolate a variable. Let us first isolate mass to solve for velocity.

`m=26.1/v` (this is equation1)

`m=400/v^2` (this is equation2)

And because mass is equal we can combine the equations to solve for v.

`26.1/v = 400/v^2`

`v = 400/26.1`

`v = 15.32 m/s` away from the launcher.

Finally, we can solve for mass by plugging our velocity back in to the momentum equation You could also find it other ways too.

`p = m * v`

`26.1 = m * 15.32`

`m = 1.70 kg`