Answer to Question #96380 in Mechanics | Relativity for Robert Perales

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 30.9 m/s. The first
snowball is thrown at an angle of 51◦
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 1

The formula for the range of projectile is

$$R=\frac{v^2}{g}\sin{2\theta}$$

In our case only the angle will be different.

We can see that:

$$\sin{2\theta}=\sin{2(90-\theta)}$$

So, cthe second angle is

$$\theta'=90-\theta=90-51=39\degree$$