Question

It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point P at a distant r from the point of projection. The product of the times taken to reach this point in the two possible ways is then proportional to

Solution

Correct option is

r

 

The range of a projectile is  the two possible angles of projection are θ and . The time of flight corresponding to these two angles are 

             

 

Thus t1t2 ∝ r.

SIMILAR QUESTIONS

Q1

At what angle (θ) with the horizontal should a body be projected so that its horizontal range equals the maximum height it attains?

Q2

 

A body is projected horizontally from a point above the ground. The motion of the body is described by the equations  

                          x = 2t

and                    y = 5 t2  

Where x and y are the horizontal and vertical displacements (in m) respectively at time t. The trajectory of the body is

Q3

 

A body is projected at time t = 0 from a certain point on a planet’s surface with a certain velocity at a certain angle with the planet’s surface (assumed horizontal). The horizontal and vertical displacement x and y (in metres) respectively vary with time t

(in seconds) as           

                             

                            

What is the magnitude and direction of the velocity with which the body is projected?