# 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.

##### 1 Answer

#### Explanation:

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:

This becomes:

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

If

So the angle to the horizontal is given by: