KinematicsHard
Question
Particles are projected from the top of a tower with same speed at different angles as shown. Which of the following are True ?
Options
A.All the particles would strike the ground with (same) speed.
B.All the particles would strike the ground with (same) speed simultaneously.
C.Particle 1 will be the first to strike the ground.
D.Particle 1 strikes the ground with maximum speed.
Solution
Let final vel be V2
Now v2x = horizontal component of velocity
V2 x = Vcos θ & V22y = (V sin θ)2 + 2 (− g) (− H)
∴ V22y = V2 sin2θ + 2 gH
⇒ V22 = V22x + V22y
= (V cos θ )2 + [V2 sin2θ + 2gH]
V22 = V2 + 2 gH
i.e., V =
This magnitude of final velocity is independent on θ
⇒ all particles strike the ground with the same speed.
i.e., ′A′ is correct.
In vertical motion
The highest velocity (initial) along the direction of displacement is possessed by particle (1). Hence particle (1) will reach the ground earliest. [since ay and sy are same for all]
i.e., ′C′ is correct
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