Neal (75 kg), a beginning skier, gets a little too ambitious and loses control o

Question

Neal (75 kg), a beginning skier, gets a little too ambitious and loses control on the slope. When he reaches the bottom he is moving horizontally at 4.8 m/s just before he collides with young Conny (35 kg) who is standing still on her skis, facing away from him on a flat spot. As he grabs her and hangs on for dear life, the two of them coast up a gentle slope that makes an angle of 5 degrees with the horizontal. At these speeds, we can ignore air resistance.

a)  Identify (and briefly explain) the relevance or irrelevance to this problem of the

following concepts: projectile motion, motion with constant acceleration, work- energy theorem, conservation of linear momentum, elastic collision, inelastic collision, gravitational potential energy.

b)  What is their speed immediately after the collision?

c)  If there is no friction, how far will they travel up the slope before coming to a

stop?

d)  How far will they travel if there is a coefficient of friction of 0.15 between their

skis and the snow?

Explanation / Answer

1) here we are applying conservation of energy , conservation of momentum

it is an inelastic collision

there involves a motion with constant acceleration

2) Applying conservation of momentum:

m1v1 = (m1+m2)*v2

==> 75*4.8 = (75+35)v2

==> v2 = 3.27 m/s

3) By conservation of energy, kinetic energy = potential energy.::

mgh = 0.5*m*v^2

==> h = v^2/2g = (3.27)^2/2*9.8 = 0.5455 m

So distance travelled is h/sin (theta)

==> d = 0.5455/Sin5 = 6.25 m

4) By conservation of energy, kinetic energy = potential energy + work done by friction.::

0.5*m*v^2 = mgdsin(theta) - u*m*g*cos(theta)*d

d = (3.27^2)/[2*(g*sin(theta)-ugcos(theta)] =(3.27^2)/[2*(0.15*9.8*cos(5 degrees)+9.8*sin(5 degrees)]

==> d=2.3059 m

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