A 20 kg cannonball is fired from a 2.4 x 103 kg. If the cannon recoils with a velocity of 3.5 m/s backwards, what is the velocity of the cannonball?
To find the velocity of the cannonball, we can use the principle of conservation of momentum.
The formula for momentum is:
momentum = mass * velocity
Since the cannonball and the cannon are initially at rest, the total momentum before firing is zero. Therefore, the momentum after firing should also be zero, as momentum is conserved.
The initial momentum of the cannonball can be calculated as:
initial momentum of cannonball = mass of cannonball * velocity of cannonball
And the initial momentum of the cannon can be calculated as:
initial momentum of cannon = mass of cannon * velocity of cannon
Since the total momentum before firing is zero, we can write the equation:
initial momentum of cannonball + initial momentum of cannon = 0
mass of cannonball * velocity of cannonball + mass of cannon * velocity of cannon = 0
Substituting the given values:
20 kg * velocity of cannonball + 2.4 x 103 kg * (-3.5 m/s) = 0
Simplifying the equation:
20 kg * velocity of cannonball = 2.4 x 103 kg * 3.5 m/s
20 kg * velocity of cannonball = 8400 kg m/s
Dividing both sides of the equation by 20 kg:
velocity of cannonball = 8400 kg m/s / 20 kg
velocity of cannonball = 420 m/s
Therefore, the velocity of the cannonball is 420 m/s.
To find the velocity of the cannonball, we can use the principle of conservation of momentum.
The principle states that the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system.
Before the cannonball is fired, the total momentum of the system (cannonball + cannon) is zero, as both the cannonball and the cannon are initially at rest.
After the cannonball is fired, the cannon recoils backward with a velocity of 3.5 m/s. Let's assume the velocity of the cannonball is v (unknown).
From the principle of conservation of momentum, we can write:
(mass of cannonball) x (velocity of cannonball) + (mass of cannon) x (velocity of cannon) = 0
(20 kg) x v + (2.4 x 10^3 kg) x (-3.5 m/s) = 0
Solving this equation for v, we get:
20v = 2.4 x 10^3 x 3.5
v = (2.4 x 10^3 x 3.5) / 20
v ≈ 420 m/s
Therefore, the velocity of the cannonball is approximately 420 m/s.
20*V-2.4E3*3.5=0
solve for V