A projectile leaves theground with initial speed v0 at an angle alpha with the h

Question

A projectile leaves theground with
initial speed v0 at an angle alpha with the horizontal. Theprojectile
reaches a maximum height H, and it lands back on the ground ata
distance L away for the starting point. What is the ratio between Hand
L? The purpose of the homework is to apply the generic equationsof
motion that we wrote many times on the board to a very specificcase.
As you work out the homework, try to keep in mind that my maininterest
is not in the result or the answer (which I do know) but on findingout
how you think and work. Pay attention to what you write, beconsistent,
and be creative if you can.

Explanation / Answer

   Maximum height attained by aprojectile    H   =   v02* sin2 / 2 *g                              -----------(1)    While the horizontal range is    L   =   v02* sin (2) /g                                 -----------(2)    Dividing equation (1) by equation (2)    H /L      =      (v02* sin2 / 2 * g) / {v02 *sin (2) / g}                   =   sin2 / 2 * sin (2)                   =   sin2 / 2 * 2 * sin * cos                              (sin 2   =   2 * sin *cos )                   = (1/4) * tan

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