A projectile is shot from the ground at a velocity of #5 m/s# and at an angle of #(7pi)/12#. How long will it take for the projectile to land?
The only force acting on the projectile after being fired is the force of gravity.
We may resolve the motion into 2 components :
In the horizontal (X) direction, there is constant velocity of
Note that we take the angle with the horizontal axis as the reference angle and so the projectile is actually being fired backwards with a projection angle of
In the vertical (Y) direction, there is constant acceleration due to gravity and hence the equations of motion for uniform acceleration in 1 direction are valid.
The initial velocity in the y-direction is hence
Therefore, time taken to reach maximum height is given by :
Therefore the total time taken to reach ground again, since the path is symmetric, is