After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +2.5 m/s. Miranda runs after her at a velocity of +4.7 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 72 kg, and Miranda's is 42 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.
momentum conservation.
Initial=final
MassA*2.5+MassM*4.7=(massA+massM)V
solve for V
To calculate the speed of Ashley and Miranda sliding together on the inner tube, we can apply the principle of conservation of momentum. In this case, since there are no external forces acting on the system, the total momentum before Miranda hops on the inner tube will be the same as the total momentum after she hops on.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the initial momentum of Ashley and the final momentum of Ashley and Miranda together, and set them equal to each other.
The initial momentum of Ashley can be calculated as:
Initial momentum of Ashley = mass of Ashley * velocity of Ashley
Given that the mass of Ashley is 72 kg and the velocity of Ashley is 2.5 m/s:
Initial momentum of Ashley = 72 kg * 2.5 m/s = 180 kg m/s
Now, let's calculate the final momentum of Ashley and Miranda together. Since Miranda hops onto the inner tube and they both slide together, their combined mass and velocity need to be considered.
The final momentum of Ashley and Miranda together can be calculated as:
Final momentum of Ashley and Miranda = (mass of Ashley + mass of Miranda) * velocity of Ashley and Miranda together
Given that the mass of Miranda is 42 kg and the velocity of Ashley and Miranda together is the same as Ashley's velocity (as mentioned in the question), which is 2.5 m/s:
Final momentum of Ashley and Miranda = (72 kg + 42 kg) * 2.5 m/s = 114 kg * 2.5 m/s = 285 kg m/s
Since the initial momentum and the final momentum must be equal according to the conservation of momentum, we have:
Initial momentum of Ashley = Final momentum of Ashley and Miranda
180 kg m/s = 285 kg m/s
Now, we can solve for the velocity of Ashley and Miranda together:
Velocity of Ashley and Miranda together = Final momentum of Ashley and Miranda / (mass of Ashley + mass of Miranda)
Velocity of Ashley and Miranda together = 285 kg m/s / (72 kg + 42 kg) = 4.5 m/s
Therefore, Ashley and Miranda will slide together on the inner tube at a speed of 4.5 m/s.