Question

One strategy in a snowball fight is to throw a snowball at a high angle over level ground. While your opponent is watching this first snowball, you throw a second snowball at a low angle and time it to arrive at the same time as the first. Assume both snowballs are thrown with the same initial speed 32.3 m/s. The first snowball is thrown at an angle of 72◦ above the horizontal. At what angle should you throw the second snowball to make it hit the same point as the first? The acceleration of gravity is 9.8 m/s 2 . Answer in units of ◦ .

Answer 1

Answer:

In order to hit the same point with the second ball, you should throw it at an angle of 18° above the horizontal.

Explanation:

Horizontal reach formula for projectiles tells us

$d=\frac{v_i^2\sin(2\theta)}{g},$

where $v_i$ is the initial velocity and $\theta$ the angle above the horizontal.

Since for both shots the reach must be the same, we have

$\frac{v_i^2\sin(2\theta_1)}{g}=\frac{v_i^2\sin(2\theta_2)}{g}\\\sin(2\theta_1)=\sin(2\theta_2)\\\theta_2=\frac{1}{2}\arcsin(\sin(2\theta_1))=\frac{1}{2}\arcsin(\sin(2\times 72\deg))=\mathbf{18\deg}$.