A skier is enjoying the mountain air while standing on a snowy slope inclinded a

Question

A skier is enjoying the mountain air while standing on a snowy slope inclinded
at 30 degrees when he suddenly notices a huge snowball rolling down at him. By the time he notices the ball, it is
only 100 m away and is traveling at 25 m/s. The skier instantly accelerates to 10 m/s and then skies directly
down the slope with acceleration g sin theta. You may assume that the snowball rolls without slipping and that
it maintains a spherical shape with moment of inertia given by I =2/5MR^2
as it rolls.
a) The snowball grows in mass and radius as it rolls. Explain how this will affect your answer.
b) Does the skier get away?

Explanation / Answer

a. With the snowball growing in size, the moment of inertia will go on increasing. The velocity however will stay the same. Hence as far as the time taken is concerned, there will be no change.

b.For the ball to not reach the skier, let us assume relative velocity and acceleration

Assuming skier at rest, the acceleration of the snow ball is -gsin theta

Its velocity is 25 m/s and the distance is 100m

100= 25t-4.9t^2

t= 2.55102+ 3.72833i

t= 2.55102- 3.72833i

The values of t we are getting are imaginary, hence the ball wont reach him

So, the skier gets away.

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