A small object is projected from level ground with an initialvelocity of magnitude 16.0 m/s and directed at an angle of 60.0 abovethe horizontal. (a) What is the horizontal displacement of the objectwhen it is at its maximum height? How does your result compare to thehorizontal range R of the object? (b) What is the vertical displacementof the object when its horizontal displacement is 80.0% of its horizontalrange R? How does your result compare to the maximum height hmaxreached by the object? (c) For when the object has horizontal displacementx - x0 = aR, where a is a positive constant, derive an expression(in terms of a) for (y - y0)/hmax. Your result should not depend on theinitial velocity or the angle of projection. Show that your expressiongives the correct result when a = 0.80, as is the case in part (b). Alsoshow that your expression gives the correct result for a = 0, a = 0.50,and a = 1.0.
A small object is projected from level ground with an initial
velocity of magnitude 16.0 m/s and directed at an angle of 60.0 above
the horizontal. (a) What is the horizontal displacement of the object
when it is at its maximum height? How does your result compare to the
horizontal range R of the object? (b) What is the vertical displacement
of the object when its horizontal displacement is 80.0% of its horizontal
range R? How does your result compare to the maximum height hmax
reached by the object? (c) For when the object has horizontal displacement
x - x0 = aR, where a is a positive constant, derive an expression
(in terms of a) for (y - y0)/hmax. Your result should not depend on the
initial velocity or the angle of projection. Show that your expression
gives the correct result when a = 0.80, as is the case in part (b). Also
show that your expression gives the correct result for a = 0, a = 0.50,
and a = 1.0.
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