← Physics · Unit 1
Projectile motion — three parts.
A ball is launched from ground level at 20 m/s, angled 30° above the horizontal. Find the answers in order. Each part unlocks the next.
1Initial velocity components
What is the initial horizontal velocity, vx?
Break the launch velocity into x and y components. vx = v cos θ.
v = 20 m/s, θ = 30°. Find vx in m/s.
m/s
cos(30°) = √3 / 2 ≈ 0.866. Multiply 20 by 0.866.
2Time of flight
How long is the ball in the air?
The ball lands at the same height it was launched from. Total time = 2 vy / g.
vy = v sin θ. Find total time in seconds, g = 9.8 m/s².
s
vy = 20 · sin(30°) = 10. Time of flight = 2·10 / 9.8 ≈ 2.04 s.
3Range
How far does the ball travel horizontally?
Range = vx · total time. Use the vx from part 1 and the time from part 2.
Range = vx · t. Find the answer in meters.
m
vx ≈ 17.32, t ≈ 2.04. Multiply them.
Nice. You just solved a full projectile problem in three structured steps — exactly how it works on an exam. Back to dashboard →