A projectile is shot from the ground at an angle of #(5 pi)/12 # and a speed of #5/7# #ms^-1#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
The initial velocity of the projectile is
This initial velocity is very small, so we are likely to be dealing with small distances and times throughout this calculation. Making this kind of estimation is helpful in checking our answers.
Our first step is to find the horizontal and vertical components of the initial velocity:
The nature of projectile motion (at least when we simplify it by ignoring air resistance) is that the horizontal velocity,
Our next step is to find the time until the maximum height is reached.
The horizontal distance traveled in this time will be:
The vertical distance traveled will be found through:
Now that we know how far the projectile has traveled horizontally and vertically, our old friend Pythagoras can give us the total distance traveled:
This is our final answer.