Question

At what angle should a slingshot be oriented for maximum altitude? For maximum horizontal range?

Answer 1

From horizontal, `90^@` and `45^@` respectively.

Explanation:

This type of motion is called projectile motion.
In such motions the height attained is given by,
`H=(u^2*sin^2theta)/(2g)`
So `H_max` is attained when `sin^2theta` is maximum. So `theta=90^@`.
and, range is given by,
`R=(u^2*sin(2theta))/g`
So `R_max` is attained when `sin(2theta)` is maximum. So `theta=45^@`.
Here, `u` is the initial speed and `g` is the acceleratin due to gravity.