Consider a projectile fired at an initial velocity at firing angle of above the ground. Ignore air resistance or the effects of a rotational effects of the Earth.
Part 1: Calculate the time it takes for the projectile to land at the same altitude.
Part 2: Calculate the range of the projectile in terms of , , and .
Part 3: Calculate the maximum altitude that the projectile is able to attain.
This problem must be analyzed in two directions.
Treat the initial point . There is no acceleration in the x-direction, and the acceleration in the x-direction is .
Since the projectile lands at the same altitude, the displacement in the y-direction is 0.
This means the two times in which are and . Of course the second time is the landing time.
Since , the range of the projectile is
The top of the trajectory occurs at half the time of landing, so
Substitute this time to the displacement equation in the y-direction.