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A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

Escape from Planet Earth

How fast would you have to throw a ball upwards so that it would never land?

Cannon Balls

How high will a ball taking a million seconds to fall travel?

Angle of Shot

Age 16 to 18
Challenge Level

Why do this problem?

This problem gives students the opportunity to investigate projectile motion in a real-life context.


Possible approach

Pose the first question, to work out the optimum angle of release for the shot, bearing in mind that the shot is released from above ground level - perhaps discuss and agree as a group what height to assume the release takes place.

Once students have tackled this first question, ask them to identify the different assumptions they have made. The key assumption is that equal force can be applied at all release angles. Invite students to speculate what variables affect the force (and hence velocity) with which the shot can be launched.

Introduce the equation for release velocity varying with angle, and then invite students to calculate the range for different launch angles. This is best done numerically, as a spreadsheet task.


Key questions

What are our modelling assumptions?
Are our assumptions valid?


Possible extension

Students may be interested in reading the article Modelling Assumptions in Mechanics.


Possible support

Cannon Balls could provide a good introduction to thinking about the mechanics of motion under gravity.