Projectile motion
Which launch angle takes a projectile furthest?
One comparison at a time
Experiment with a guide
Compare height and range without confusing a higher launch with a longer launch.
Comparison 1 of 3
Start with a low angle
We launch at 20 m/s and 30° above the ground. Motion combines horizontal advance and rising/falling. Gravity changes vertical velocity.
Advance 0,25 s or play. Compare the moving point with the dashed trajectory.
You are exploring other values. You can continue freely or apply this comparison’s values again.
How to read this drawing
x measures horizontal distance and y measures height, in metres. The point is the object; the dashed curve shows the complete predicted path. On reaching the ground, the object stops. In the comparison, both attempts use the same clock. Arrow v₀ marks the initial direction. The axes use the same scale, but framing changes with the values.
From drawing to graph
What changes? Let’s compare.
A line shows the relationship between quantities. The point marks your choice or the instant in the animation. First read the axis names and units.
One experiment at a time
Save. Change. Compare.
Save the current values, change one quantity and observe both lines on the same graph. The saved line is dashed. The attempt stays in this browser.
Compare the chosen values
What if… Compare angles of 30° and 60° at the same initial speed. The range is equal, but what about the height?
What is happening?
A projectile combines uniform horizontal motion with vertical motion accelerated by gravity.
Gravity changes the vertical component of velocity, while the horizontal component stays constant in this model. A larger angle gives more height and flight time, but less horizontal speed. For the same initial speed, the greatest range occurs at 45° when launch and landing heights are equal.
v₀ — initial speed (m/s) · θ — angle · g = 9.81 m/s²
The model and its limits
No air resistance, constant gravitational acceleration of 9.81 m/s², and equal launch and landing heights. The graph uses the same scale on both axes and adjusts its view to fit the trajectory.