A ball rolls without slipping down the track as shown in the figure below, starting from...
A ball rolls without slipping down the track as shown in the
figure below, starting from rest at a height h1
= 24 m as shown. The ball is traveling horizontally when it leaves
the bottom of the track, which has a height h2
= 9.5 m. Find where the ball hits the ground; that is, find
L.
Homework Answers
?Y = X*tan? + ( (g*X^2) / 2(Vi*cos?)^2 )
in your problem Y= -9.5 m (downward)
theta= 0
then
1/2 m Vi^2 = m g h because the PE at the top is converted to KE at
the bottom and h here is 14.5 m (difference from top to bottom of
the track)
the m's cancel
so
Vi = sqrt(9.81*14.5 / 0.5 ) = 16.8 m/s
then substitute
-9.5 = X*0 + ( (-9.81 * x^2) / 2(16.8 * 1)^2 )
solve for X i.e 23.38 m
Without the figure, I can tell you only that the ball (assumed
to be solid) has a velocity at h2 of
V = ?[2*g*(h1 - h2)/(1.4)] = 12.04 m/s
If the ball is hollow, use 1.667 in the eq above.
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