At what angle should you throw the second snowball to make it hit the same point as the first?

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 34.6 m/s. The first snowball is thrown at an angle of 68◦ 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

Since the parabolic path is symmetric above & below the 45 degree angle, the distance from the 45 degree to 68 degrees is 23 degrees.

45 -23 = 22 degrees. So if you throw the snowball at 22 degrees, it would go the same distance (84.8 m).

However, you would throw the second snowball later (6.54-2.643) = 3.9 seconds later to have the snowballs hit at the same time!