Prove that the maximum horizontal range is 4 times the maximum height attained by a projectile.

The horizontal range is maximum when the angle of projection is 45°.

So,

        ...(1)

Maximum height for angle of projection 45 degree is,

              ...(2) 

Therefore, from equation (1) and (2),

                      R = 4H

That is, range is 4 times the maximum height attained by a projectile. 

890 Views

A projectile is fired with ‘kinetic energy K at an angle θ with the horizontal. What will be the kinetic energy of projectile at the highest point?

Let a projectile of mass m be projected with velocity u at an angle θ.

Kinetic energy of projection, 

At the highest point, vertical component of velocity is zero and there is only horizontal component of velocity.

Horizontal component = u cos θ.

∴ Kinetic energy at the highest point is,

 K.E =
    
183 Views

A man sitting near the window of a moving train drops a stone. Describe the path of stone on seeing by a man standing near the track.

The stone which is dropped from moving train has same horizontal velocity as that of train with respect to the track. Therefore, for a person standing near the track, stone will act like a horizontal projectile and path followed is parabola. 
130 Views

There are two angles of projection for which horizontal range is same. Prove that the sum of maximum heights for these two angles is independent of angle of projection.

Given, horizontal range is same for two angles of projection. 

The angles are θ and 90°–θ.

Maximum height H1 for angle projection θ is,

                      

Maximum height H2 for angle projection 90°–θ is, 

           

Now, sum of maximum height is,  

     

Hence the result.

209 Views

Advertisement

A body is projected with velocity u at an angle θ and reaches the ground at time T. What will be the time of flight if the body is projected with same speed at an angle (90°–θ)?


Time of flight for angle of projection is given by,
 
                                              ...(1)

If the body is projected at an angle , then the time of flight T' is

                ...(2)

Dividing (2) by (1), we get

           
114 Views

Advertisement
Advertisement