a water balloon launcher with a mass of 4 kg fires a .5 balloon with a velocity of 3m/s to the east. what is the recoil velocity of the launcher?

its 0.38 m/s west. timothy is incorrect.

3.0 west

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

According to the principle of conservation of momentum, the total momentum before the launch is equal to the total momentum after the launch. In this case, the total momentum includes the momentum of the launcher and the momentum of the water balloon.

The momentum can be calculated using the equation:

Momentum (p) = mass (m) × velocity (v)

Before the launch:
Momentum of the launcher (L) = mass of the launcher (m1) × velocity of the launcher (v1)
Momentum of the balloon (B) = mass of the balloon (m2) × velocity of the balloon (v2)

After the launch:
Momentum of the launcher (L') = mass of the launcher (m1) × recoil velocity of the launcher (v')

Since the water balloon is fired in only one direction (to the east), we consider its velocity as positive. However, the recoil velocity of the launcher will be in the opposite direction (to the west), so we consider it as negative.

Given:
Mass of the launcher (m1) = 4 kg
Velocity of the launcher (v1) = 0 m/s (since it is at rest initially)
Mass of the balloon (m2) = 0.5 kg
Velocity of the balloon (v2) = 3 m/s (to the east)

Using the principle of conservation of momentum, we can write:
Momentum before launch = Momentum after launch

(m1 × v1) + (m2 × v2) = (m1 × v') + (m2 × -v')

Plugging in the given values:
(4 kg × 0 m/s) + (0.5 kg × 3 m/s) = (4 kg × v') + (0.5 kg × -v')

0 kg·m/s + 1.5 kg·m/s = 4 kg·v' - 0.5 kg·v'

1.5 kg·m/s = 4 kg·v' - 0.5 kg·v'

Now, let's solve for the recoil velocity of the launcher (v').

1.5 kg·m/s + 0.5 kg·v' = 4 kg·v'

0.5 kg·v' - 4 kg·v' = -1.5 kg·m/s

-3.5 kg·v' = -1.5 kg·m/s

v' = (-1.5 kg·m/s) / (-3.5 kg)

v' ≈ 0.43 m/s

Therefore, the recoil velocity of the launcher is approximately 0.43 m/s to the west.

To determine the recoil velocity of the launcher, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces are acting on the system.

In this case, the water balloon launcher (which includes the water balloon and the launcher itself) is the system we are considering. Initially, the launcher and the water balloon are at rest, so the total momentum before the event is zero.

To calculate the recoil velocity of the launcher, we need to find the momentum of the water balloon. The momentum of an object can be calculated by multiplying its mass (m) by its velocity (v). Given that the mass of the water balloon is 0.5 kg and its velocity is 3 m/s to the east, we can calculate its momentum as follows:

Momentum of water balloon = mass of water balloon × velocity of water balloon
= 0.5 kg × 3 m/s
= 1.5 kg·m/s to the east

Since momentum is conserved, the total momentum after the event should also be zero. Therefore, the launcher must have a recoil velocity in the opposite direction of the water balloon.

Considering the conservation of momentum, we can set up the following equation:

Total momentum before = Total momentum after

0 = momentum of launcher + momentum of water balloon

0 = mass of launcher × recoil velocity of launcher + 1.5 kg·m/s

Since the mass of the launcher is given as 4 kg, we can rearrange the equation to find the recoil velocity of the launcher:

recoil velocity of launcher = - (momentum of water balloon) / (mass of launcher)
= -1.5 kg·m/s / 4 kg
= -0.375 m/s to the east

Therefore, the recoil velocity of the launcher is 0.375 m/s to the east. The negative sign indicates its direction is opposite to that of the water balloon.