A 50kg gun mounted on wheels shoots a 3kg missile directed at an angle of 30 with a horizontal.if the muzzle velocity of missile is 550m/s what is the horizontal recoil velocity of the gun.
To find the horizontal recoil velocity of the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing of the missile is equal to the total momentum after the firing.
The momentum of an object is calculated by multiplying its mass by its velocity.
Before firing, the gun and the missile are at rest. So the initial momentum is zero.
After firing, the gun starts moving in the opposite direction of the missile to maintain momentum conservation.
Let's denote the recoil velocity of the gun as Vg, and the final velocity of the missile as Vm.
The horizontal momentum before firing: 0 (since both gun and missile are at rest)
The horizontal momentum after firing: (50 kg) * (-Vg) + (3 kg) * cos(30°) * (550 m/s)
According to conservation of momentum:
0 = (50 kg) * (-Vg) + (3 kg) * cos(30°) * (550 m/s)
To find Vg, we can rearrange the equation:
Vg = (3 kg) * cos(30°) * (550 m/s) / (50 kg)
Let's calculate it:
Vg = (3 kg) * cos(30°) * (550 m/s) / (50 kg)
Vg = 0.900 m/s
So the horizontal recoil velocity of the gun is approximately 0.900 m/s.