Chapter 3, Problem 8QAP

To determine

(a)

The angle at which the longest range is achieved by projectile.

To determine

(b)

The angle at which the longest time of flight is achieved.

To determine

(c)

The angle at which the greatest height of flight is achieved.

The angle at which the greatest height is achieved by projectile is $\theta =90°$.

Calculation:

When the projectile will reach maximum height then the vertical component of velocity will be zero,

  $\begin{array}{c}{v}_o{}^2\sin \theta -2gh=0\\ h=\frac{{\left(v_o\sin \theta \right)}^2}{2g}\end{array}$

The maximum value of h will exist when $\sin \theta =1\text{or}\theta =90°$.