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?

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Question

 

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?

Solution

Correct option is

20 ms –1 at an angle of 30o with the horizontal

 

We know that the position coordinates x and y are given by 

                         

  

Comparing Eq. (i) with  we have,

 Also, comparing Eq. (ii) with y = 10t – t2, we have, v0 sin θ = 10 ms–1. These equations give  which gives θ = 30o.

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SIMILAR QUESTIONS

Q1

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
easy View solution
Q2

At what angle (θ) with the horizontal should a body be projected so that its horizontal range equals the maximum height it attains?
easy View solution
Q3

 

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
easy View solution