A ball is thrown with initial speed v0 up an inclined plane. The plane is inclined at an angle φ above the horizontal, and the ball is launched at an angle α > φ above the horizontal. (a) How much time does it take for the ball to land? (b) How far up the hill will the ball land? (c) For what angle α will the range from part (b) be a maximum?
A ball is thrown with initial speed v0 up an inclined plane. The plane is inclined
at an angle φ above the horizontal, and the ball is launched at an angle α > φ above the
horizontal. (a) How much time does it take for the ball to land? (b) How far up the hill will
the ball land? (c) For what angle α will the range from part (b) be a maximum? (d) What is
the maximum range? [Note: This problem could be solved in a standard horizontal/vertical
coordinate system. It may be easier, however, to choose coordinates such that ˆx points up
the slope and ˆy is normal to the slope. Then explicitly integrate the equations of motion in
this coordinate system to find the ball’s position as a function of time.]
For each part, check that your results make sense for various limiting values of α and/or φ
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