A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s- 1 and the stone still hits the bird while descending, then the horizontal velocity of stone is

Question

A stone is projected from a point on the ground in such a way so as to hit a bird at height 3h and could attain a maximum height 4h above the ground. If at the instant of projection, the bird flies away horizontally with speed 10 m s- 1 and the stone still hits the bird while descending, then the horizontal velocity of stone is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-6banzknznbgm.png" /> (A) 8ms- 1 (B) 15 m s- 1 (C) 12 ms- 1 (D) 9 m s- 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-6banzknzvs97.png" /> Particle taken t1 time to reach from 0 to 3h and also t1 to reach from 3h to 4h and yet again t1 time from 4h to 3h. ∴ vx3t1-10× 3t1=vxt1 ⇒ vx = 15 ms- 1

$8 m s^{- 1}$

$15 m s^{- 1}$

$12 m s^{- 1}$

$9 m s^{- 1}$

Particle taken $t_{1}$ time to reach from 0 to $3 h$ and also $t_{1}$ to reach from $3 h$ to $4 h$ and yet again $t_{1}$ time from $4 h$ to $3 h .$
$∴ v_{x} 3 t_{1} - 10 \times 3 t_{1} = v_{x} t_{1}$
$\Rightarrow v_{x} = 15 m s^{- 1}$

8ms−1

15ms−1

12ms−1

9ms−1

Particle taken t1​ time to reach from 0 to 3h and also t1​ to reach from 3h to 4h and yet again t1​ time from 4h to 3h. ∴vx​3t1​−10×3t1​=vx​t1​ ⇒vx​=15ms−1

$8 m s^{- 1}$

$15 m s^{- 1}$

$12 m s^{- 1}$

$9 m s^{- 1}$

Particle taken $t_{1}$ time to reach from 0 to $3 h$ and also $t_{1}$ to reach from $3 h$ to $4 h$ and yet again $t_{1}$ time from $4 h$ to $3 h .$
$∴ v_{x} 3 t_{1} - 10 \times 3 t_{1} = v_{x} t_{1}$
$\Rightarrow v_{x} = 15 m s^{- 1}$