After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of 2.7 m/s. Miranda runs after her at a velocity of 4.1 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube?

After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of 2.7 m/s. Miranda runs after her at a velocity of 4.1 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 71 kg and Miranda's is 58 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.

SOLUTION:

mass of Ashley (Ma) = 71 kg

mass of Miranda (Mm) = 58 kg

initial velocity of Ashley (Va) = 2.7 m/s

initial velocity of Miranda (Vm) = 4.1 m/s

Find the final velocity (Vf) at which they both slide together

from the conservation of momentum, initial momentum = final momentum

Ma.Va + Mm.Vm = (Ma + Mm) . Vf

[tex]Vf = \frac{Ma.Va + Mm.Vm}{Ma + Mm} \\ Vf=\frac{(71 x 2.7) + (58 x 4.1)}{71+58}[/tex]

Vf = (191.7 +237.8) / (129)

Vf = 3.3 m/s