Question

A stone is projected from a point on the ground so as to hit a bird on the top of a vertical pole of height h and attain a maximum height 2h above the ground. If at the instant of projection the bird flies away horizontally with a uniform speed and if the stone hits the bird while descending then the ratio of the speed of the bird to the horizontal speed of the stone is

Answer 1

Explanation:

Maximum height of the projectile is given by the expression

h

max

=

2g

v

0

2

sin

2

θ

⇒2h=

2g

v

0

2

sin

2

θ

⇒v

0

=

sinθ

2

gh

...................(i)

∵y=v

0

sinθt−

2

1

gt

2

⇒h=

sinθ

2

gh

sinθt−

2

1

gt

2

⇒gt

2

−4

ght

+2h=0

t=

2g

4

gh

±

16gh−8gh

=

2g

4

gh

±2

2gh

⇒t

1

=

g

h

(2−2

2

) and t

2

=

g

h

(2+

2

)

At these two times , the projectile is at the same height as the bird.

let v be the speed of the bird , for bird to be hitted Therefore,

vt

2

=v

a

cosθ(t

2

−t

1

)

⇒

v

0

cosθ

v

=

t

2

t

2

−t

1

=

2

+1

2

I hope it will help you