rvanveshana.com
t = 0.00s
Height (m)Range (m)
Horizontal Vel (v_x) Vertical Vel (v_y)

Live Telemetry & Summary

Observe the live values changing in real-time as the simulation runs. Tweak parameters and press **Simulate** to see new calculations.

Time:0.00 s
Distance (x):0.0 m
Height (y):0.0 m
Vert Speed (v_y):14.1 m/s
Total Speed (v):20.0 m/s

Variable Adjuster

Initial Speed (vā‚€)20m/s
540
Launch Angle (Īø)45Ā°
090
Gravity (g)9.8m/sĀ²
225

Projectile Kinematics Lab

PROJ

Projectile motion simulates an object launched into a gravitational field. The motion is separated into horizontal translation (constant velocity) and vertical acceleration (constant gravity acceleration).

x(t)=v0xt,y(t)=v0ytāˆ’12gt2x(t) = v_{0x}t, \quad y(t) = v_{0y}t - \frac{1}{2}gt^2

Whiteboard Solver Steps

Step 1

Initial Velocity Decomposition

The initial velocity vector is decomposed into horizontal (constant) and vertical components.

v0x=v0cosā”(Īø)=14.14 m/s,v0y=v0sinā”(Īø)=14.14 m/sv_{0x} = v_0 \cos(\theta) = 14.14 \text{ m/s}, \quad v_{0y} = v_0 \sin(\theta) = 14.14 \text{ m/s}
Step 2

Time of Flight

The total time the projectile spends in the air before hitting the ground.

tflight=2v0yg=2Ɨ14.149.8=2.89 st_{flight} = \frac{2v_{0y}}{g} = \frac{2 \times 14.14}{9.8} = 2.89 \text{ s}
Step 3

Peak Height and Range

The maximum vertical altitude achieved and the total horizontal travel distance.

ymax=v0y22g=10.20 m,R=v02sinā”(2Īø)g=40.82 my_{max} = \frac{v_{0y}^2}{2g} = 10.20 \text{ m}, \quad R = \frac{v_0^2 \sin(2\theta)}{g} = 40.82 \text{ m}