1. A 0.50 kg ball is moving with a velocity of 8.0 m/s along a horizontal floor. It hits another ball with a mass of 0.80 kg and moving at 10.0 m/s in the opposite direction. If the first ball bounces back with a velocity of 12 m/s, with what velocity and in what direction will the second ball go after collision?
2. A cannon mounted on the back of a ship fires a 50.0 kg cannonball in the horizontal direction at a speed of 150 m/s. IF the cannon and ship to which it is firmly attached have a mass of 4.00 x 103 kg and are initially at rest, what is the speed of the ship just after shooting the cannon? Ignore water resistance. 1.9 m/s opposite cannonball’s velocity.
1. To find the velocity and direction of the second ball after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass with its velocity. So, the momentum of the first ball before the collision is given by:
Momentum of first ball before collision = mass of first ball * velocity of first ball
= 0.50 kg * 8.0 m/s
= 4.0 kg*m/s
Similarly, the momentum of the second ball before the collision is:
Momentum of second ball before collision = mass of second ball * velocity of second ball
= 0.80 kg * (-10.0 m/s) [negative sign indicates opposite direction]
= -8.0 kg*m/s
The total momentum before the collision is the sum of these two momenta:
Total momentum before collision = Momentum of first ball before collision + Momentum of second ball before collision
= 4.0 kg*m/s - 8.0 kg*m/s
= -4.0 kg*m/s
Now, let's find the total momentum after the collision by considering the velocities of the two balls after the collision.
Momentum of first ball after collision = mass of first ball * velocity of first ball after collision
= 0.50 kg * 12 m/s
= 6.0 kg*m/s
Using the law of conservation of momentum, we can set the total momentum before the collision equal to the total momentum after the collision:
Total momentum before collision = Total momentum after collision
-4.0 kg*m/s = 6.0 kg*m/s + Momentum of second ball after collision
Solving for the momentum of the second ball after the collision:
Momentum of second ball after collision = -4.0 kg*m/s - 6.0 kg*m/s
= -10.0 kg*m/s
Finally, to find the velocity of the second ball after the collision, we divide the momentum by the mass:
Velocity of second ball after collision = Momentum of second ball after collision / mass of second ball
= (-10.0 kg*m/s) / 0.80 kg
= -12.5 m/s
Therefore, the second ball will move with a velocity of 12.5 m/s in the opposite direction after the collision.
2. To find the speed of the ship just after shooting the cannon, we can again use the law of conservation of momentum. Since the cannon and the ship form a closed system, the total momentum before firing the cannon should be equal to the total momentum after firing.
The momentum of an object is calculated by multiplying its mass with its velocity. So, the momentum of the cannonball before firing is:
Momentum of cannonball before firing = mass of cannonball * velocity of cannonball
= 50.0 kg * 150 m/s
= 7500 kg*m/s
Since the cannon and the ship are initially at rest, their total momentum before firing is zero.
Total momentum before firing = 0 kg*m/s
Now, let's find the total momentum after firing the cannon. The cannonball shoots off in the horizontal direction, so the momentum of the cannonball after firing is:
Momentum of cannonball after firing = mass of cannonball * velocity of cannonball after firing
= 50.0 kg * 150 m/s
= 7500 kg*m/s
The momentum of the ship after firing is given by:
Momentum of ship after firing = mass of ship * velocity of ship after firing
Since the ship is firmly attached to the cannon, the momentum of the ship is equal in magnitude but opposite in direction to the momentum of the cannonball.
Momentum of ship after firing = - Momentum of cannonball after firing
= -7500 kg*m/s
Using the law of conservation of momentum, we can set the total momentum before firing the cannon equal to the total momentum after firing:
Total momentum before firing = Total momentum after firing
0 kg*m/s = 7500 kg*m/s + (-7500 kg*m/s) + Momentum of ship after firing
Simplifying, we find:
Momentum of ship after firing = 0 kg*m/s
Finally, to find the velocity of the ship after firing, we divide the momentum by the mass:
Velocity of ship after firing = Momentum of ship after firing / mass of ship
= (0 kg*m/s) / (4.00 x 103 kg)
= 0 m/s
Therefore, the ship will have a speed of 0 m/s just after shooting the cannon.