A projectile is shot from the ground at an angle of #pi/8 # and a speed of #2 /7 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
There are several approaches to this type of question. The most direct method is to find time
Projectiles follow a parabola, assuming (as most questions do) that air resistance is negligible. In a parabola, the slope is 0 at the vertex, which is the peak, or turnaround point between going up and coming down.
So any time a projectile question says "maximum height" you know that
To solve a projectile problem like this we need both horizontal and vertical components of the velocity, which we can get using trigonometry:
Using kinematics equations, we can find
That's a pretty feeble projectile!
There is another solution, which is faster, but is more indirect. We can exploit the fact that parabolas are symmetrical, so we can also find the total horizontal range, and divide by 2.
There is a formula for horizontal range, but it must be used cautiously - it only applies when the start and end height are the same, ie a flat surface.