Launch an idea
Projectile motion
Launch a ball, trace its path, and see how angle and speed change its flight.
Projectile motionTRY IT YOURSELF
Range40.775 m
Peak height10.194 m
Flight time2.883 s
Horizontal speed14.142 m/s
Teal + amber · follow the changing valuesIdealized physics model
What if you changed…
Try a starting point
Compare 30° and 60° at the same speed. What stays the same?
See the calculation
x = v₀ cos(θ)t · y = v₀ sin(θ)t − ½gt²
- Horizontal velocity = 20 cos(45°) = 14.14 m/s.
- Vertical launch velocity = 20 sin(45°) = 14.14 m/s.
- Flight time = 2vᵧ/g = 2.88 s. Range = vₓ × time = 40.77 m.
What this model assumes
Point particle launched and landing at the same height; uniform gravity and no air resistance.
Keep an eye on this
A 45° launch gives maximum range only with a level landing and no air resistance.
Understand the physics ↗A little question. A clearer picture.
Projectile motion: common questions
Wondering about the why? Start here.
Why is 45° the best launch angle here?
For a level landing, range is v₀² sin(2θ)/g. The sine term reaches 1 when 2θ is 90°, so θ is 45°.
Does a heavier ball travel farther?
Mass does not appear in this ideal model. Air resistance can make real trajectories depend on mass, size, and shape.