A ball is fired at a speed of 8 m/s at 20˚ above the horizontal from the top of a 5 m high wall. How far from the base of the ball will the ball hit the ground? Also calculate the angle below horizontal the velocity vector makes.
To get the time of flight we can use:
Using the convention that "down is +ve" this becomes:
This simplifies to:
Applying the quadratic formula:
Ignoring the -ve root this gives:
We can now get the range d from the horizontal component of velocity which is constant:
To get the angle to the horizontal which the ball strikes the ground we need the vertical component of its velocity when it lands.
We can use:
See fig (b):
We now know:
If we needed the resultant we could use Pythagoras, however we are only asked for the angle to the horizontal
So the angle to the horizontal is given by: