General & First-year
Projectile Lab
Set the launch angle, speed and gravity, then fire. The trajectory animates and labels itself; toggle air resistance to see drag bend the path and shorten the range. Ghost trails let you compare shots.
63.8 m
Range
16.0 m
Max height
3.61 s
Time of flight
The method, with your numbers
Constant-acceleration kinematics
- 1
Resolve the launch velocity
vₓ = v·cos θ v_y = v·sin θ
vₓ = 25·cos 45° = 17.68 m/s v_y = 25·sin 45° = 17.68 m/s
Horizontal and vertical motion are independent — solve them separately.
- 2
Time to the apex (v_y reaches 0)
t_apex = v_y / g
t_apex = 17.68 / 9.81 = 1.8 s
At the top of the arc the vertical velocity is exactly zero.
- 3
Maximum height
h = v_y² / (2g)
h = 17.68² / (2·9.81) = 15.93 m
- 4
Time of flight (symmetric arc)
T = 2·v_y / g
T = 2·17.68 / 9.81 = 3.6 s
Launch and landing are at the same height here, so T is exactly twice the apex time.
- 5
Range
R = vₓ·T
R = 17.68·3.6 = 63.71 m
45° gives the maximum range in a vacuum — you're at the optimum.
Drag any control above — every number here recalculates. Want this method for any problem? Step Sheets →
Gravity
9.81 m/s²
How to use this simulation
Set the launch angle, speed and gravity, then fire. The trajectory animates and labels itself; toggle air resistance to see drag bend the path and shorten the range. Ghost trails let you compare shots.
Everything runs in your browser — no sign-up, no download. Change a value and the result updates instantly, so you can build a feel for how each input shapes the outcome. It pairs with Crameleon's practice exams and step sheets when you want to go from intuition to working the problems.