Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and Junior as they move across the ice after the collision
momentum is conserved
25 * 8 = v * (25 + 55)
To find the speed of Ben and Junior after the collision, we can use the principle of conservation of momentum. The equation for momentum is:
Momentum = mass x velocity
Since Ben and Junior embrace after the collision, we can assume they move together as one unit. Let's denote their combined mass as M and their combined velocity as V after the collision.
Before the collision, Junior was moving with a speed of 8 m/s. After the collision, Ben and Junior move together with a common speed V, so their combined mass M is the sum of their individual masses:
M = massOfBen + massOfJunior
= 55 kg + 25 kg
= 80 kg
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. So, we can write:
Momentum before collision = Momentum after collision
The momentum before the collision is the product of Junior's mass and his initial velocity:
Momentum before collision = massOfJunior x velocityOfJunior
= 25 kg x 8 m/s
= 200 kg m/s
The momentum after the collision is the product of the combined mass (M) and the common velocity (V):
Momentum after collision = M x V
Now, we can equate the two expressions for momentum to find the velocity after the collision:
200 kg m/s = 80 kg x V
Solving for V:
V = (200 kg m/s) / (80 kg)
= 2.5 m/s
Therefore, the speed of Ben and Junior as they move across the ice after the collision is 2.5 m/s.