Solving Projectile problems

The common factor between the two independent motions of an object that is travelling both vertically and horizontally is t ; the time for which it is travelling. It is important not to confuse the horizontal velocity and displacement with those that apply to the vertical motion.

Consider this problem.
A ball is thrown horizontally with a speed of 15.0 m s^–1 from a vertical height of 18.0 m. How far has it travelled horizontally when it reaches the ground?
Take g = 10.0 m s^–2.

To solve this problem:

• apply the equations of motion with uniform acceleration to the vertical motion to find the time that the ball is in the air. Note that vertically u = 0.
• use the constant speed equation to calculate the distance travelled horizontally by the ball in this time.

Check that this gives an answer of 27 m.

A common error in solving this type of problem is to take u, the initial vertical velocity, to be equal to the value of the horizontal velocity.