Q1. A projectile is launched at 20 m/s at 30°. Find its maximum height (g = 10).
H = u²sin²θ/2g
H = 20² × (sin30°)² / (2×10) = 400 × 0.25 / 20
H = 5 m
Motion in a Plane — Class 11
Add motion in two directions and you get projectiles. Explore vectors and use the projectile calculator for range, height and time of flight.
Scalars & vectorsScalars have only magnitude (mass, speed); vectors have magnitude and direction (displacement, velocity, force).
Projectile motionMotion under gravity with a horizontal launch component. The path is a parabola; horizontal velocity is constant, vertical changes with g.
Range, height & timeFor launch speed u at angle θ: R = u²sin2θ/g, H = u²sin²θ/2g, T = 2u sinθ/g. Range is maximum at 45°.
Uniform circular motionMotion in a circle at constant speed but changing direction, needing a centripetal acceleration a = v²/r towards the centre.
Projectile calculator Interactive
Set the launch speed and angle to get the range, maximum height and time of flight (g = 9.8 m/s²).
Range, R—m
Max height, H—m
Time of flight, T—s
Range is maximum at 45°. Complementary angles (e.g. 30° and 60°) give the SAME range.
Numericals practice Interactive
Projectile problems with steps (g = 10 m/s²).
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Solved numericals
Q2. A car goes round a circular track of radius 50 m at 10 m/s. Find its centripetal acceleration.
a = v²/r
a = 10² / 50
a = 2 m/s²
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Range of a projectile | R = u² sin2θ / g | m |
| Maximum height | H = u² sin²θ / 2g | m |
| Time of flight | T = 2u sinθ / g | s |
| Centripetal acceleration | a = v² / r | m/s² |
Common mistakes & exam wins
- Horizontal and vertical motions of a projectile are independent; solve them separately.
- Horizontal velocity stays constant (no horizontal force); only the vertical velocity changes with g.
- Range is maximum at 45°; complementary angles give equal ranges.
- In uniform circular motion speed is constant but velocity is not (direction changes).
Frequently asked questions
What is projectile motion?
The motion of an object thrown into the air under gravity alone, following a parabolic path with constant horizontal velocity and changing vertical velocity.
At what angle is the range maximum?
At 45°, because R = u²sin2θ/g is maximum when sin2θ = 1, i.e. 2θ = 90°.
What is centripetal acceleration?
The acceleration directed towards the centre of a circular path, a = v²/r, that keeps a body moving in a circle.