A water-balloon launcher with mass 5 kg fires a 1 kg balloon with a velocity of 8 m/s to the east. What is the recoil velocity of the launcher?

1.6 west

To find the recoil velocity of the launcher, we can use the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, the system consists of the water-balloon launcher and the balloon.

According to the conservation of momentum, the initial momentum of the system is equal to the final momentum of the system.

The initial momentum of the system is given by the equation:
Initial momentum = (mass of launcher) * (velocity of launcher)

The final momentum of the system is given by the equation:
Final momentum = (mass of launcher) * (velocity of launcher) + (mass of balloon) * (velocity of balloon)

Since the mass of the launcher is 5 kg, the mass of the balloon is 1 kg, and the velocity of the balloon is 8 m/s to the east, we can substitute these values into the equation to find the final momentum:

Final momentum = (5 kg) * (velocity of launcher) + (1 kg) * (8 m/s)

Now, since the initial momentum is equal to the final momentum, we can set these two expressions equal to each other and solve for the velocity of the launcher:

(5 kg) * (velocity of launcher) = (5 kg) * (velocity of launcher) + (1 kg) * (8 m/s)

Simplifying this equation, we get:

0 = (1 kg) * (8 m/s)

Therefore, the recoil velocity of the launcher is 0 m/s. This means that the launcher does not experience any recoil motion.

To find the recoil velocity of the launcher, we can use the principle of conservation of momentum. According to this principle, the total momentum before the balloon is launched should be equal to the total momentum after the balloon is launched.

The momentum of an object is given by the product of its mass and velocity. So, before the balloon is launched, the total momentum is the sum of the momentum of the launcher and the momentum of the balloon. After the balloon is launched, the total momentum is the sum of the momentum of the launcher and the momentum of the balloon in the opposite direction (as the launcher recoils).

Let's assume that the initial velocity of the launcher is v (which we need to find), and the mass of the launcher is M (given as 5 kg). The mass of the balloon is m (given as 1 kg), and its velocity is V (given as 8 m/s).

So, before the balloon is launched:
Total momentum = Momentum of the launcher + Momentum of the balloon
= M * v + m * 0 (as the balloon is stationary initially)

After the balloon is launched:
Total momentum = Momentum of the launcher in opposite direction + Momentum of the balloon
= -M * V + m * V (since the balloon moves in the opposite direction with velocity V)

According to the principle of conservation of momentum:
Total momentum before = Total momentum after

M * v + m * 0 = -M * V + m * V

Simplifying the equation:
M * v = (m + M) * V

Now, we can substitute the known values into the equation and solve for v.

M = 5 kg
m = 1 kg
V = 8 m/s

5 kg * v = (1 kg + 5 kg) * 8 m/s

5 kg * v = 6 kg * 8 m/s

5v = 48

v = 48 / 5

v ≈ 9.6 m/s

Therefore, the recoil velocity of the launcher is approximately 9.6 m/s to the east.

East velocities +

momentum before = 0
so momentum after = 0
1 * 8 + 5 * v = 0

v = 8/5 west