Question

If a projectile is shot at an angle of `(5pi)/12` and at a velocity of `19 m/s`, when will it reach its maximum height??

Answer 1

The projectile will reach its maximum height when the velocity equals zero.

Explanation:

At an angle of `((5pi)/12)`, the initial velocity forms the hypotenuse of a right-angled triangle with angle `((5pi)/12)` at the base.
The maximum height of the shot will be the vertical component `(y)`, of the initial velocity vector of `19` m/s, and will occur when the final velocity equals zero.
The initial velocity of the vertical component is `Voy = 19sin((5pi)/12) = 0.434` m/s.
Using `V = Vo + at` we can rearrange to find `t`:

`t = (V - Vo)/a`

`= (0 - 0.434)/- 9.8 = 0.04 s`

Assuming that the force due to gravity is in the downward direction, therefore, the upward direction has a negative sign.