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
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
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.
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.