Question

A Knight of the Round Table fires off a vat of burning pitch from his catapult at 14.5 m/s, at 33 ◦ above the horizontal. The acceleration of gravity is 9.8 m/s 2 . How long is it in the air? Answer in units of s

Answer 1

How long it is in the air depends on the times it takes the acceleration due to gravity to bring it to the ground.

The vat has a vertical upward velocity, so the acceleration due to gravity must counteract this velocity, bringing it to zero , which is the highest point reached by the vat, and then bring it to the ground. The neat thing is that it is going to hit the ground with the same vertical velocity with which it was fired, so you can find the times it takes the final vertical velocity to be equal to zero, multiply that value by two, and you're done.

You need to find that vertical velocity first and then find the time.

Answer 2

1) Draw a carefully labeled diagram including coordinate systems
2) Resolve the initial velocity into horizontal and vertical components.
3) Apply kinematic equations to motion in the y direction to get the time to reach max heigt.
4) assuming no air resistence, total time of flight is 2 times time to get to max height

Answer 3

Yep. That is the way the problem can be solved.

The kinematic equation must be one that allows to find the time, and you can plug the initial (vertical) velocity, the acceleration (due to gravity) and the final (vertical) velocity (which we know is going to be zero).