A catapult used by medieval armies hurls a stone of mass 32.0 kg with a velocity of 50.0 m/s at a 30.0 degree angle above the horizontal. What is the horizontal distance traveled when the stone returns to its original height? Ignore air resistance. Check your calculator deg/rad mode.

The horizontal distance traveled when the stone returns to its original height = 220.81 m

Explanation:

Considering vertical motion of catapult:-

At maximum height,

Initial velocity, u = 50 sin30 = 25 m/s

Acceleration, a = - 9.81 m/s²

Final velocity, v = 0 m/s

We have equation of motion v = u + at

Substituting

v = u + at

0 = 25 - 9.81 x t

t = 2.55 s

Time of flight = 2 x Time to reach maximum height = 2 x 2.55 = 3.1 s

Considering horizontal motion of catapult:-

Initial velocity, u = 50 cos30 = 43.30 m/s

Acceleration, a = 0 m/s²

Time, t = 5.10 s

We have equation of motion s = ut + 0.5 at²

Substituting

s = ut + 0.5 at²

s = 43.30 x 5.10 + 0.5 x 0 x 5.10²

s = 220.81 m

The horizontal distance traveled when the stone returns to its original height = 220.81 m