Shoot the Monkey Lab · Level 2

Predict, test, measure and explain. Work through the six steps and their quick checks, then complete the lab missions in the simulator.

Step 1 of 6 · The puzzle

A hunter, a monkey, and one tricky question

A monkey hangs from a branch. A hunter points a dart rifle straight at it. The monkey is clever: the moment it sees the flash of the rifle, it lets go of the branch and drops.

So where should the hunter aim?

  • Above the monkey?
  • Below the monkey, where it will be?
  • Straight at the monkey?

Your guess Pick one before you go on. We'll come back to it.

aim line ?

Step 2 of 6 · Idea one

With no gravity, the dart flies in a straight line

Imagine the whole scene floating in deep space, where nothing pulls things down. The dart leaves the rifle and keeps going in exactly the direction it was pointed. The monkey lets go but just floats in place.

The dart travels along the aim line and hits the monkey. Easy.

This is Newton's first law: a moving object keeps moving in a straight line at a steady speed unless a force acts on it.

Quick check In deep space, after the dart leaves the rifle, it…

No gravity: dart stays on the line

Step 3 of 6 · Idea two

Gravity pulls everything down the same way

Now switch gravity back on. Gravity pulls every object downward, and it speeds them up by the same amount every second, no matter how heavy they are or how fast they are moving sideways.

Drop a ball and throw another one sideways at the same moment. They hit the floor at the same time. The sideways motion and the downward fall happen independently.

This ignores air resistance, which is small for a dart and a short fall.

Quick check A dart twice as heavy is fired the same way. Compared with the light dart, it falls…

dropped thrown sideways same height, same moment

Step 4 of 6 · Putting it together

The dart and the monkey fall by the same amount

Think of the dart's motion as two parts added together:

  1. Where it would be with no gravity: somewhere on the straight aim line.
  2. How far gravity has pulled it down from that spot.

The monkey starts falling at the very same instant, so gravity has pulled it down by exactly the same distance. Both drop together, and the dart arrives at the monkey's new, lower position.

Answer: aim straight at the monkey.

Quick check If the dart is fired twice as fast, will it still hit?

fall orange = gravity's pull

Step 5 of 6 · The numbers

How far does something fall?

Starting from rest, the distance an object falls in time t is

fall = ½ × g × t²

g is the strength of gravity: about 9.8 m/s² on Earth. The fall grows with the square of time, so things fall faster and faster.

Time t½ × 9.8 × t²Fall
0.5 s½ × 9.8 × 0.251.2 m
1.0 s½ × 9.8 × 14.9 m
1.5 s½ × 9.8 × 2.2511.0 m
2.0 s½ × 9.8 × 419.6 m

The same formula applies to the monkey and to the dart's drop below the aim line. That is the whole trick.

Quick check How far does something fall in 3 s on Earth? (g = 9.8 m/s²)

Worked example

Tree 28 m away. Monkey 12 m up. Rifle held 1.5 m up. Dart speed 32 m/s.

  1. Aim angle: rise 10.5 m over 28 m≈ 20.6°
  2. Dart's sideways speed: 32 × cos 20.6°≈ 30.0 m/s
  3. Time to reach the tree: 28 ÷ 30.0≈ 0.93 s
  4. Monkey's fall: ½ × 9.8 × 0.93²≈ 4.3 m
  5. Dart's drop below the aim line: ½ × 9.8 × 0.93²≈ 4.3 m
  6. Both end up at 12 − 4.3≈ 7.7 m high

The monkey needs ½ × 9.8 × t² = 12 m to reach the ground, which takes about 1.56 s. The dart gets there in 0.93 s, so it hits.

Step 6 of 6 · Your turn

Your lab tasks

In this level you work like a scientist. For every shot:

  1. Predict hit or miss and give a reason. The rifle won't fire until you do.
  2. Observe what happens and compare it with your prediction.
  3. Explain the result by answering the question the lab asks you.

Every shot adds a row to your data table and a point to a graph of drop against t². You will use the graph to measure g yourself. Then complete the six missions and write your final explanation.

Remember

Qualitatively: gravity pulls the dart and the monkey down together, so aiming straight works.

Quantitatively: after time t, both have fallen ½gt². The hit only fails if the monkey reaches the ground first, when ½gt² is larger than its height.