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How big is your target?

By David, 27 August 2013 Activity

Learn some handy sporting tips on how to aim with this hands-on maths activity.

You will need

A person holding a squash ball. In the background, there is a jar. The jar and the ball appear the same width.

Hold the squash ball about a metre from the jar. Close one eye, then move closer or further away until the two look the same size.

  • Squash ball
  • Jar
  • Bucket
  • Clean bin
  • Pen or pencil
  • Paper

What to do

  1. Find a large flat area outside and put the jar on the ground.
  2. Crouch down about a metre from the jar. Hold the squash ball at arm’s length. Close one eye, then look at the jar and the squash ball. Move towards or away from the jar until the two look the same size.
    A tally sheet. Heading:Jar. In Jar: 3. In line: 5. Miss: 2

    Try to throw the squash ball into the jar ten times. Record your results.

  3. Open your closed eye and mark your spot with the stick.
  4. Stand behind the stick and try to throw the squash ball into the jar. Repeat ten times. Record how many went in, how many were in line but didn’t go in, and how many missed completely.
  5. Repeat steps 1 to 4 with the bucket instead of the jar, remembering to record your results.
  6. Then, repeat steps 1 to 4 with the bin instead of the jar, remembering to record your results.

What’s happening?

A person holding a squash ball. In the background, there is a bucket. The bucket and the ball appear the same width.

Go through these steps again with the bucket, then the bin.

In this activity, you probably found that about the same number of throws were in line to hit for each target. If you had tried throwing at the same sized targets over different distances, the closer targets would have been much easier than the far away ones.

When you compared how the targets looked with the ball, you weren’t comparing size, instead you were comparing angles. A squash ball 40 mm wide held roughly one metre from your eye takes up about two degrees. That means any throw you make within those two degrees will be in line with the target.

Applications

In this activity, you are measuring angular diameter. Angular diameter links size and distance. If you know how large something is, you can use its angular diameter to work out how far away it is. Golfers need to know how far away the hole is before they play a shot. So, there’s a flag in the hole, and they know how big the flag is. This helps them estimate the distance to the hole.

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