Crocodile Jump: Projectile Physics for Kids

Every jump is two motions happening at once

When the crocodile leaps off the riverbank, gravity and its launch speed act completely independently of each other, and that separation is the whole secret to projectile motion. Sideways, nothing is pulling the crocodile back or forward, so its horizontal speed stays exactly the same from takeoff to landing. Downward, gravity pulls at a constant 9.8 metres per second squared the entire time it's in the air, whether it's moving fast or slow sideways. Galileo was the first to prove this split cleanly, nearly 400 years ago, by rolling balls off tables and timing their fall.

live demo · adjust launch angle and power to land the jump● LIVE

The two equations that decide everything

Once the crocodile leaves the bank at speed v and angle θ above the water, its horizontal and vertical positions at any later time t follow two completely separate rules:

x(t) = v · cos(θ) · t                     (sideways: constant speed)
y(t) = v · sin(θ) · t − ½ · g · t²      (up-down: constant pull of gravity)

Put those two together and the path traced out is a parabola — the same curve for a thrown ball, a kicked football, or a crocodile jumping a river. The height climbs, slows, stops rising for an instant at the very top, then falls back down, speeding up the whole way, and it always lands at the same height it took off from in exactly twice the time it took to reach the peak.

Why 45 degrees is the magic angle

For a fixed launch speed, the jump distance (the range) depends on the angle through the formula range = v²·sin(2θ)/g, and sin(2θ) is largest, equal to 1, exactly when θ = 45 degrees. That is why 45 degrees gives the longest possible jump for any given power — too flat and the crocodile barely leaves the water before splashing back down, too steep and most of its energy goes straight up instead of forward. Interestingly, any two angles that add up to 90 degrees (like 30 and 60) land at exactly the same distance, just with very different flight times and heights.

More power, more distance

Because range depends on the square of the speed (v²), doubling the crocodile's launch power more than doubles how far it jumps — it actually quadruples the distance, at the same angle. That squared relationship is why animals that need to cover a lot of ground, or athletes in the long jump, care so much about generating extra speed at takeoff: small gains in speed pay off much faster than small gains in angle once you're already reasonably close to 45 degrees.

What the simulation lets you try

Drag the angle and power sliders and watch the same two rules play out every time: the horizontal line the crocodile covers stretches or shrinks with cos(θ) and v, while the height of the arc grows with sin(θ) and v. Try 20 degrees, 45 degrees and 70 degrees at the same power and compare — the 45-degree jump should carry the crocodile the farthest across the river every single time.

Frequently asked questions

Why does the crocodile go the farthest at a 45 degree launch angle?

The jump distance is proportional to sin(2 times the angle), and that value is at its maximum, 1, exactly when the angle is 45 degrees. Angles either flatter or steeper than that both reduce the horizontal distance, for the same launch speed.

Do gravity and sideways speed affect each other during the jump?

No, and that's the key idea behind projectile motion. Horizontal speed stays constant throughout the whole jump since nothing pushes or slows it sideways, while gravity pulls straight down the entire time regardless of how fast the crocodile is moving sideways. The two combine into the parabola shape without interfering with each other.

Does doubling the crocodile's jump power double how far it goes?

It quadruples it, not doubles it, because jump distance depends on the square of the launch speed. So a crocodile that launches twice as fast, at the same angle, lands about four times farther across the river.

Try it live

Everything above runs in your browser — open Crocodile Jump and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Crocodile Jump simulation

Why 45 Degrees Is the Best Jumping Angle