Why 45° throws the farthest
Every throw splits its speed between going up and going forward. Find the perfect split.
Throw a ball as hard as you can. Where does it land? That depends on two things: how fast you throw it, and which way you point it. Today we keep the speed the same and change only the angle.
Try it first
Every shot below leaves at exactly 20 metres per second. Fire a few different angles and look at the list underneath. Which one wins?
Did 45° win? It should have. Here is why.
Every throw has two jobs
When you launch a ball, its speed gets split into two parts:
- Going forward. This part carries the ball across the ground.
- Going up. This part keeps the ball in the air. Gravity slowly eats it away, and when it runs out the ball comes back down.
The ball only travels forward while it is in the air. So you need both: enough forward speed to cover ground, and enough upward speed to stay up long enough.
Too low, too high, just right
Point it low (15°). Almost all the speed goes forward, but there is hardly any upward speed. Gravity pulls the ball down in just over a second. Fast, but it lands early.
Point it high (75°). Now most of the speed goes up. The ball hangs in the air for four whole seconds, but it barely moves forward while it is up there.
Point it at 45°. The speed is split evenly. The ball stays up long enough and moves forward fast enough. That balance gives the longest throw.
Here are the numbers from the launcher above:
| Angle | Time in the air | Highest point | Distance |
|---|---|---|---|
| 15° | 1.3 s | 2.9 m | 25.0 m |
| 30° | 2.2 s | 6.6 m | 37.7 m |
| 45° | 3.0 s | 11.7 m | 42.2 m |
| 60° | 3.6 s | 16.8 m | 36.2 m |
| 75° | 4.0 s | 20.5 m | 20.8 m |
Look at 30° and 60°. They land close together, and so do 15° and 75°. Angles that add up to 90° make a matching pair. One takes a low, quick path and the other takes a high, slow one. In Launch Lab, Mission 3 uses this trick to get over a wall.
Why aren't the pairs exactly equal?
Good spotting if you noticed! Our launcher sits 1.5 metres above the ground, like a ball leaving your hand. That gives the low shots a tiny head start. If you launched from right on the ground, 30° and 60° would land in exactly the same spot.
The maths, for when you're ready
Scientists write the rule like this, for a launch from ground level:
distance = speed² × sin(2 × angle) ÷ g
Here, g is the pull of gravity: 9.81 on Earth. The sin part is biggest when 2 × angle is 90°, which happens when the angle is 45°. That's the whole secret in one line.
Does this work in real life?
Mostly. Real balls push through air, which slows them down. Air resistance means the best angle for a real throw is usually a little lower than 45°. Shot-putters, for example, often launch at around 35° to 40°. But the idea of splitting your speed between up and forward always holds.