A particle is projected with velocity at such an angle that it just clears two walls of equal height h which are at a distance 2h from each other. Show that time of passing between the two walls is
A stone is projected with velocity (√2gh) from the top of building h meter high. Show that it will fall farthest at a distance (2√2)h.
The situation is as shown in figure. Let w.r.t. A (point of fire of first shot), the position of bird is
Position of first shot at any instant:
As both the shots hit the bird simultaneously, therefore at the instant of hitting positions of both the shots will be same.
i.e.
From condition we get
Let the body be projected with velocity u making an angle θ with the horizontal.
The direction of motion of body after t seconds of throw is given by the equation,
Here at time, t = 3 the value of is and at t = 5s the value of is
∴ ...(1)
and
...(2)
From (2),
...(3)
Substituting in equation (1), we get
...(4)
The horizontal range of the body,
Therefore, the body falls at a distance of 200 from the point of projection.