Throw the ball: speed and angle
"Throw the ball: speed and angle" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "Projectile motion" in Motion in a Plane. Set the speed and the angle. The dots show the ball every 0.2 s; the green arrows are its horizontal velocity, the red ones its vertical velocity. Horizontal velocity is constant, vertical velocity falls by g each second. R = v₀² sin 2θ₀/g: largest at 45°, equal for complementary angles. JEE Main asked 40 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Projectile motion in Motion in a Plane. Change the values and watch what happens.
In JEE Main
42 shifts analysed
40 questions from Motion in a Plane across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §3.9
- A projectile is an object that, once thrown, moves under gravity alone; air resistance is neglected. Its motion is a uniform horizontal motion and a uniformly accelerated vertical motion, independent of each other.
- Launched at speed v₀ at angle θ₀ above the horizontal: aₓ = 0, aᵧ = −g; x = (v₀ cos θ₀) t and y = (v₀ sin θ₀) t − ½ g t².
- The horizontal velocity v₀ cos θ₀ never changes; the vertical velocity vᵧ = v₀ sin θ₀ − g t falls by g every second and is zero at the top.
- The path is y = (tan θ₀) x − g x² / [2 (v₀ cos θ₀)²], a parabola.
- Time to the top tₘ = v₀ sin θ₀ / g; time of flight T_f = 2 v₀ sin θ₀ / g; maximum height hₘ = (v₀ sin θ₀)² / 2g; horizontal range R = v₀² sin 2θ₀ / g.
- The range is largest at θ₀ = 45°, Rₘ = v₀²/g. Angles 45° + α and 45° − α (complementary angles such as 30° and 60°) give the same range but different heights and times.
- A ball thrown at 20 m/s at 30° (g = 9.8 m/s²) rises 5.1 m, stays up 2.04 s and lands 35.3 m away.
- Thrown horizontally from a height h, a body falls for t = √(2h/g) whatever its horizontal speed: from 4.9 m it takes 1.0 s, and at 10 m/s it lands 10 m away moving at 14 m/s.
Questions
3 answers
- What does the "Throw the ball: speed and angle" simulation show?
- Set the speed and the angle. The dots show the ball every 0.2 s; the green arrows are its horizontal velocity, the red ones its vertical velocity.
- Does JEE Main ask questions from Motion in a Plane?
- Yes. JEE Main asked 40 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Projectile motion" in Motion in a Plane (Class 11 Physics).
Embed this simulation
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.