☰ Contents · Physics

Transmission of motion and the horizontally thrown body

Lessons 5–6 · 2 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 10, 1st edition. Niso Poligraf Publishing House, Tashkent, 2017
6

Motion of a body thrown horizontally

Textbook: pp. 16–18
GoalCalculate the time of flight, range, velocity and trajectory of a body thrown horizontally.
New words
horizontally thrown body · gorizontal otilgan jismrange · uchish uzoqligiparabola · parabolavelocity components · tezlikning tashkil etuvchilari
Explanation

A body thrown horizontally from height h with speed υ₀ takes part in two independent motions: uniform motion horizontally (x = υ₀t, υₓ = υ₀) and free fall from rest vertically (y = h – gt²/2, υᵧ = gt). The time to hit the ground depends only on the height: t = √(2h/g); the range is s = υ₀t = υ₀√(2h/g). The trajectory equation is y = h – g·x²/(2υ₀²), a parabola. The speed on landing is υ = √(υₓ² + υᵧ²) = √(υ₀² + 2gh); its angle with the horizontal is tanα = υᵧ/υₓ = gt/υ₀. In curved motion the displacement is not equal to the path: the displacement is the straight segment joining the start and end points, the path is the distance along the trajectory. Both the magnitude and the direction of the velocity vector keep changing.

Worked examples
A body is thrown horizontally from h = 80 m with υ₀ = 30 m/s (g = 10 m/s²). t = √(2·80/10) = 4 s; s = 30·4 = 120 m; on landing υᵧ = 10·4 = 40 m/s, υ = √(30² + 40²) = 50 m/s.
A stone thrown horizontally from the edge of a cliff lands 60 m away after 3 s. The initial speed is υ₀ = s/t = 60/3 = 20 m/s; the launch height is h = gt²/2 = 10·9/2 = 45 m.
Class activity

With the teacher: gently flick one ball horizontally off a table edge while releasing a second one straight down at the same moment. Listen to the landing sounds: do they land together? Explain with the principle of independence. Collect the balls from the floor; never throw them at anyone.

Practice
1
What curve is the trajectory of a horizontally thrown body?
2
A body is thrown horizontally at υ₀ = 12 m/s from h = 80 m (g = 10 m/s²). What is the range (m)? (t = 4 s)
3
A body is thrown horizontally from h = 45 m at υ₀ = 40 m/s (g = 10 m/s²). What is the vertical velocity υᵧ on landing (m/s)? (t = 3 s)
4
Why does the fall time of a horizontally thrown body not depend on the launch speed?