Question

A skater with a mass of 72 kg is traveling east at 5.8 m/s when he collides with another skater of mass 45 kg heading 60° south of west at 12 m/s. If they stay tangled together, what is their final velocity?

Answer 1

The final velocity of the skaters after the collision is 4.2 m/s.

How to calculate the final velocity of the skaters?

The final velocity of the skater is calculated by applying the principle of conservation of linear momentum as follows.

sum of initial momentum = sum of final momentum

(72 kg x 5.8 m/s x cos0) - (45 kg x 12 m/s x cos 60) = vx (72 kg + 45 kg)

where;

• vx is the final velocity of the skaters after the entanglement in x - direction

147.6 = 117vx

vx = 147.6 / 117

vx = 1.26 m/s

(72 kg x 5.8 m/s x sin0) + (45 kg x 12 m/s x sin 60) = vy (72 kg + 45 kg)

467.65 = 117vy

vy = 467.65 / 117

vy = 4 m/s

The resultant velocity is;

v = √ (1.26² + 4²)

v = 4.2 m/s

Answer 2

The final velocity is 5.87 m/s

Step-by-step explanation:

Given-

mass,
`m_(1)` = 72 kg

speed,
`v_(1)` = 5.8 m/s

`Mass_(2)`,
`m_(2)` = 45 kg

`speed_(2)`,
`v_(2)` = 12 m/s

Θ = 60°

Final velocity, v = ?

Applying the conservation of momentum:

`m_(1)` X
`v_(1)` +
`m_(2)` X
`v_(2)` = (
`m_(1)` +
`m_(2)` ) v

72 X 5.8 + 45 X 12 X cos 60° = (72 + 45) v

v = 417.6 + 540 X
`(0.5)/(117)`

v = 417.6 +
`(270)/(117)`

v = 5.87 m/s

The final velocity is 5.87 m/s