Question

ice skater sally is 40kg and is skating side-by-side holding onto Billy her 65 kg partner. They are moving at a velocity of 3 m/s to the left. To do a trick billy throws the Sally to the left at 5.5 m/s what is the speed of the Billy after he throws sally

Answer 1

To determine Billy's speed after throwing Sally, we apply conservation of momentum to find that his final velocity will be approximately 1.46 m/s to the left.

Step-by-step explanation:

Ice skater Sally is 40kg, and Billy is 65kg, and they are moving at a velocity of 3 m/s to the left. The conservation of momentum principle can be applied to find Billy's speed after he throws Sally. Initially, their combined momentum is the sum of their individual momenta; since they are moving together, this would just be their total mass times their shared velocity.

Initial momentum (pi) = (mass of Sally + mass of Billy) × initial velocity
pi = (40kg + 65kg) × 3 m/s
pi = 315 kg·m/s

When Billy throws Sally, the system must conserve momentum. Sally's momentum will be her mass times her new velocity, and Billy's momentum will be his mass times his new, unknown velocity.

Sally's momentum (ps) = mass of Sally × velocity of Sally
ps = 40kg × 5.5 m/s
ps = 220 kg·m/s

To find Billy's final velocity (vf), we use the conservation of momentum:

pi = ps + (mass of Billy × vf)

Substituting in the known values:

315 kg·m/s = 220 kg·m/s + (65kg × vf)

Solving for vf:

vf = (315 kg·m/s - 220 kg·m/s) / 65kg
vf = 95 kg·m/s / 65kg
vf = 1.46 m/s

Billy will be moving at a speed of approximately 1.46 m/s to the left after he throws Sally.