If the horizontal range and the max height of a body projected at an angle titre to the horizontal is K and Q respectively. Show that the muzzle velocity Vo is given by: Vo=√[2gQ + K²/8Q]​

Explanation:

Recall that

and

From Eqn(2), we can write

Using the identity , we can rewrite Eqn(1) as

Squaring the above equation, we get

Use Eqn(3) on Eqn(4) and we will get the following:

This simplifies to

Rearranging this further, we get

Putting to the left side, we get

Finally, taking the square root of the equation above, we get the expression for the muzzle velocity as

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