help me please!

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 24.1 m/s. The first snowball is thrown at an angle of 52◦ above the horizontal. At what angle should you throw the second snowball to make it hit the same point as the first? Note the starting and ending heights are the same. The acceleration of gravity is 9.8 m/s 2 .

Answer 1

Recall that the body thrown at some speed v travels the longest distance when thrown at the α=45 degrees angle, but shorter distance if the angle is less than 45 degrees (low trajectory) or larger than 45 degrees (high trajectory). The flight time is less over the lower trajectory. The time of flight is t=2vcosα/g and the distance of flight l is

l = v²sin2α/g.

Since sin2α = sin(180° - 2α) the flight distance is the same for α=52° and β=(90°- α)=38° angles. Hence, the snowball should be thrown at 38° angle.