You visited us 1 times! Enjoying our articles? Unlock Full Access!

General Gravity Problem

A stone dropp...

Question

A stone dropped from topof a building of height h and it reaches after t seconds on Earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after $t_{1}$ and $t_{2}$ seconds respectively, then

t = t₁ - t₂

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

If a stone is dropped from height h then

$h = \frac{1}{2} g t^{2}$ .....(i)

If a stone is thrown upward with velocity u then

$h = - u t_{1} + \frac{1}{2} g t_{1}^{2}$ ........(ii)

If a stone is thrown downward with velocity u then

$h = u t_{2} + \frac{1}{2} g t_{2}^{2}$ ............(iii)

From (i)(ii) and (iii) we get

$- u t_{1} + \frac{1}{2} g t_{1}^{2} = \frac{1}{2} g t^{2}$ .................(iv)

$u t_{2} + \frac{1}{2} g t_{2}^{2} = \frac{1}{2} g t^{2}$ ..................(v)

Dividing (iv) and (v) we get

$∴ \frac{- u t_{1}}{u t_{2}} = \frac{\frac{1}{2} g (t^{2} - t_{1}^{2})}{\frac{1}{2} g (t^{2} - t_{2}^{2})}$ or $- \frac{t_{1}}{t_{2}} = \frac{t^{2} - t_{1}^{2}}{t^{2} - t_{2}^{2}}$

By solving t = $\sqrt{t_{1} t_{2}}$

Suggest Corrections

Similar questions

Q. A stone is dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after

t_{1}

and

t_{2}

seconds respectively, then

Q. A stone dropped from a building of height

h

and it reaches the ground after

t

seconds. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity

u

and they reach the ground after

t_{1}

and

t_{2}

seconds respectively, then

Q. A stone is dropped from a building of height

h

and it reaches after

t

seconds on earth. From the same building if two stones are thrown, one upwards and other downwards, with the same velocity

u

and they reach the earth surface after

t_{1}

and

t_{2}

seconds respectively, then

A stone dropped from the top of a building of height $h$ . It reaches the ground after $t s$ . From the same building if two stones are thrown (one upwards and other downwards) with the same velocity $u$ , and they reach the earth surface after $t_{1}$ and $t_{2}$ seconds respectively, then

Q. A stone dropped from a building of height

h

and it reaches the ground after

t

seconds. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity

u

and they reach the ground after

t_{1}

and

t_{2}

seconds respectively, then

Join BYJU'S Learning Program

A stone dropped from topof a building of height h and it reaches after t seconds on Earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

A stone dropped from topof a building of height h and it reaches after t seconds on Earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after $t_{1}$ and $t_{2}$ seconds respectively, then