A projectile is launched with 200kg m/s of momentum and 1000 J of kinetic energy. What is the mass of the projectile.

The answer is said to be 20 kg but I can't get it. I tried this but it didn't work:

p=mv=200 m=200/v
I plugged that into this equation:
KE=1/2mv^2=1000 = 1/2(200/v)v^2=1000

Can anyone help? THanks

Nevermind, I got it.

I was solving for velocity the first time when it should have been mass.

To find the mass of the projectile, you can use the given information about momentum and kinetic energy.

1. Start with the equation for momentum: p = mv, where p is the momentum and m is the mass of the projectile. In this case, the momentum is given as 200 kg m/s.
So, p = mv = 200 kg m/s.

2. Next, use the equation for kinetic energy: KE = 1/2mv², where KE is the kinetic energy and v is the velocity of the projectile. It is given that the kinetic energy is 1000 J.
So, KE = 1/2mv² = 1000 J.

You correctly started by solving the first equation for mass (m = 200/v).

Now, substitute this expression for mass into the equation for kinetic energy:
1/2(200/v)v² = 1000.

To simplify the equation, cancel out the v in the numerator and denominator:
1/2 * 200v = 1000.

Multiply both sides by 2 to eliminate the fraction:
200v = 2000.

Divide both sides by 200:
v = 10 m/s.

Now, substitute this value of v back into the expression for mass:
m = 200/v = 200/10 = 20 kg.

Therefore, the mass of the projectile is indeed 20 kg.

To solve this problem, we need to use the formulas for momentum and kinetic energy.

Given that the momentum (p) of the projectile is 200 kg m/s and the kinetic energy (KE) is 1000 J, we can use the following equations:

1. Momentum (p) = mass (m) × velocity (v)
2. Kinetic Energy (KE) = 1/2 × mass (m) × velocity squared (v^2)

Let's start solving for the mass (m) of the projectile.

1. Rearrange the momentum equation to solve for mass:
m = p / v

2. Substitute the given values into the equation:
m = 200 kg m/s / v

3. Now, we can use the kinetic energy equation to solve for velocity (v).

1/2 × m × v^2 = KE

Substitute the given values:
1/2 × 200 kg/v × v^2 = 1000 J

Simplify the equation, cancel out the v terms:
100 kg × v = 1000 J

Divide both sides by 100 kg:
v = 1000 J / 100 kg
v = 10 m/s

Now that we know the velocity (v) is 10 m/s, we can substitute this value back into the mass equation:

m = 200 kg m/s / 10 m/s
m = 20 kg

Therefore, the mass of the projectile is indeed 20 kg.