Hard

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

Create a free account to view solution

View Solution Free

More Physics Questions

A point mass is projected, making an acute angle with the horizontal. If angle between velocity and acceleration is &#95...An object is thrown horizontally from a point ′A′ from a tower and hits the ground 3s later at B. The line f...A ball is thrown vertically upward with speed 10 m/sec and it returns to ground withspeed of 8 m/sec. There exists a con...One stone is projected horizontally from a 20 m high cliff with an initial speed of 10 ms-1. A second stone is simultane...A small ball rolls of the top of a stairway horizontally with a velocity of 4.5 m s-1. Each step is 0.2 m high and 0.3 m...