Question

After sliding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +3.0 m/s. Miranda runs after her at a velocity of +4.2 m/s and hops on the inner tube.

How fast do the two of them slide across the snow together on the inner tube? Ashley's mass is 69 kg and Miranda's is 59 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.

Answer 1

Their combined velocity on the inner tube is +3.55 m/s

Step-by-step explanation:

This question deals with the conservation of linear momentum. The total linear momentum in a closed system is conserved.

Therefore,

P_i = P_f

m₁ v₁ + m₂ v₂ = (m₁ + m₂) v₁₂

where

• m₁ is the mass of Ashley
• m₂ is the mass of Miranda
• v₁ is Ashley's velocity
• v₂ is Miranda's velocity
• v₁₂ is their combined velocity

Therefore,

v₁₂ = (m₁ v₁ + m₂ v₂) / (m₁ + m₂)

v₁₂ = ( (69 kg)(3 m/s) + (59 kg)(4.2 m/s) ) / (69 kg + 59 kg)

v₁₂ = +3.55 m/s

Therefore, Ashley and Miranda's combined velocity on the inner tube is +3.55 m/s.

The positive sign shows that the velocity is in the positive direction.