Answer to Question #309624 in Mechanics | Relativity for Nina

Question

A gold ball is given an initial speed of 20. meters per second and returns to level ground. Which launch angle above level ground results in the ball traveling the greatest horizontal distance?[Neglect friction]

Answer 1

Explanations & Calculations

• When the air resistance is insignificant it is the launch angle $\small 45^0$ either from vertical or horizontal to project any object into the air to get the maximum horizontal distance or the range for any given initial speed.
• This can be evaluated by the formula

$\qquad\qquad \begin{aligned} \small R&=\small \frac{v^2}{g}\sin2\theta\\ \small R_{max}&\to\small \sin2\theta_{max}\\ \small \sin2\theta_{max}&=\small 1=\sin90\\ \small \theta &=\small 45^0 \end{aligned}$