Question

During a snowball fight , your opponent distracts you by throwing a snowball at you in a high arc. she thriws snowballs with a speed of 24.5 m/s and the first is thrown at 70.0 degrees. As you are watching the first snowball, she throws a second at a lower angle. If both snowballs cover the same horizontal distance, at what angle should the second be thrown?

Answer 1

Answer:

Explanation:

Given

launch velocity $u=24.5\ m/s$

first ball launch angle $\theta _1=70^{\circ}$

Suppose another ball is thrown at an angle of $\theta _2$

Both ball have same range

Range of Projectile $R=\frac{u^2\sin 2\theta }{g}$

$R_1=\frac{u^2\sin 2\theta _1}{g}$

For second ball

$R_2=\frac{u^2\sin 2\theta _2}{g}$

$R_1=R_2$

$\frac{u^2\sin 2\theta _1}{g}=\frac{u^2\sin 2\theta _2}{g}$

$\sin 2\theta _1=\sin 2theta _2$

Either $\theta _1=\theta _2$ or

$2\theta _1=180-2\theta _2$

I.e. $\theta _2=90-\theta _1$

$\theta _2=90-70=20^{\circ}$

so another ball must be thrown at $20^{\circ}$