Thrown up, thrown across: air resistance changes the trip

By the end of this lesson

By the end you can describe and explain how air resistance changes the motion of a ball thrown upwards and of a projectile, and sketch the velocity–time graph and the path.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$v$	velocity

One force flips, one doesn't

Throw a ball straight up. Two forces act on it, and they behave very differently:

Weight is constant and always downwards.
Air resistance always acts opposite to the velocity, and it's zero when the ball is momentarily at rest.

So when the ball turns round at the top, the air resistance flips direction and the weight doesn't. That single fact explains everything in this lesson.

The round trip, stage by stage

Stage	Velocity	Air resistance $D$	Resultant force	Size of acceleration
Going up	upwards	downwards	$W + D$ , down	more than $g$
At the top	zero	zero	$W$ , down	exactly $g$
Coming down	downwards	upwards	$W - D$ , down	less than $g$

Notice that the acceleration is downwards at every stage, even at the top. Going up, the weight and the drag gang up on the ball; coming down, the drag fights the weight.

Worked example: Same ball, same drag, different direction

A ball of mass $0.20\ \text{kg}$ is thrown vertically upwards. At one moment on the way up, the air resistance on it is $0.50\ \text{N}$ . At a later moment, on the way down, the air resistance is again $0.50\ \text{N}$ . Find the acceleration at each moment. Use $g = 9.81\ \text{m s}^{-2}$ .

Have a go first?

Quick check

Multiple choiceQuestion 1 · Recall

CalculateQuestion 2 · Apply

Answer the 2 questions above to continue.