Question

A counterweight trebuchet is a type of catapult from the Middle Ages that uses a weight at one end to hurl a projectile. The trebuchet arm pivots about a point 4m from the ground, with the counterweight side 5m long and the projectile side 10m long.
find Theta1, the initial angle of the projectile arm, theta2, the final angle of the projectile arm( when the counterweight reaches the ground.), and theta 3, the angle that the projectile is launched at. Express all angle in radians.

Answer 1

Neat question. Lots of right angles.

Starting out, the long arm is on the ground, a hypotenuse of 10m and an opposite side of 4m, so that
sin(theta1)= 4/10=0.4,
theta1 = arc sin(0.4) =23.6o = (23.6/57.3) rad = 0.41 rad.

There are 2 pi = 6.28 radians per 360 degrees, so 1 radian is 57.3 rad.

Right after firing, the short arm is on the ground,
sin(theta2)=4/5=0.8
theta2 = 53.1o = [53.1/57.3] rad = 0.93 rad

The projectile goes off at right angle to the long arm,
thus at 90o-53.1o=36.9o = 0.64 rad.