10.2 Projectile Problems
When doing projectile problems, you can treat each direction separately or you can write them both together as vectors. Example below shows both methods.
Question 10.2.1:
A ball is thrown horizontally at 5 m s−1 out of a window 4 m above the ground.
(i) How long does it take to reach the ground?
(ii) How far from the building does it land?
(iii) What is its speed just before it lands and at what angle to the ground is it moving?
Solution 10.2.1:
Figure 10.4 shows the path of the ball. It is important to decide at the outset where the origin and axes are. You may choose any axes that are suitable, but you must specify them carefully to avoid making mistakes. Here the origin is taken to be at ground level below the point of projection of the ball and upwards is positive. With these axes, the acceleration is −g m s−2.
Figure 10.4
Method 1: Resolving into Components
(i) Position: Using axes as shown and 
Horizontally:
Vertically,
The ball reaches the ground when y = 0. Substituting in Equation 2 gives:
The ball hits the ground after 0.894 s (to 3 s.f.).
(ii) When the ball lands x = d so, from Equation 1,
d = 5t = 5 × 0.894... = 4.47...
The ball lands 4.47 m (to 3 s.f.) from the building.
(iii) Velocity: Using v = u + at in the two directions,
Horizontally
Vertically
To find the speed and direction just before it lands:
The ball lands when t = 0.894... so
The components of velocity are shown in the diagram in Figure 10.5 below.
Figure 10.5
The speed of the ball is:
It hits the ground moving downwards at an angle α to the horizontal where:
Method 2: Using Vectors
Using perpendicular vectors in the horizontal (x) and vertical (y) directions, the initial position is 
Using
and
(i) Equation 2 gives t = 0.894 and substituting this into Equation 1 gives (ii) d = 4.47.
(iii) The speed and direction of motion are the magnitude and direction of the
velocity of the ball. Using
So when t=0.894, 
Notice that in both methods the time forms a link between the motions in the two directions. You can often find the time from one equation and then substitute it in another to find out more information.