When the effect of aerodynamic drag is included, the y‐acceleration of a baseball moving vertically upward is au = −g − kv2, whi
le the acceleration when the ball is moving downward is ad = −g + kv2, where k is a positive constant and v is the speed in meters per second. If the ball is thrown upward at 30 m/s from essentially ground level, compute its maximum height h and its speed vf. upon impact with the ground. Take k to be 0.006 m−1 and assume that g is constant.
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Answer:
Explanation:
The ball will rise decreasing its speed until it reaches the highest point where its speed will be zero. From this point the tennis ball will begin to fall again, in the free fall the tennis ball will gain speed but now in the opposite direction. When it returns to the same point where it was launched, its speed will be the same as the one that was launched but with the opposite sign.
We can check this using the equation:
where
ang h is the height, but because the ball returns to the same point where it started, h =0
then
the initial and final velocity will be the same in number, but we know that the ball is going in the opposite direction, so the final velocity must have the opposite sign from the initial velocity
so if ,