A stone is allowed to fall from the top of a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the two stones meet after a time $t$.For the stone dropped from the tower:Initial velocity,$u = 0\, m/s$.Let the displacement of the stone in

Vedclass · Accepted Answer

$78.4\, m$ and $20.6\, m$

Vedclass · Answer

(D) Let the two stones meet after a time $t$.For the stone dropped from the tower:Initial velocity,$u = 0\, m/s$.Let the displacement of the stone in time $t$ from the top of the tower be $s$.Acceleration due to gravity,$g = 9.8\, m/s^2$.Using the equation of motion,$s = ut + \frac{1}{2}at^2$:$s = 0 	imes t + \frac{1}{2} 	imes 9.8 	imes t^2$$s = 4.9t^2$ ............. $(1)$For the stone thrown upwards:Initial velocity,$u = 25\, m/s$.Let the displacement of the stone from the ground in time $t$ be $s'$.Acceleration due to gravity,$g = -9.8\, m/s^2$.Using the equation of motion,$s' = ut + \frac{1}{2}at^2$:$s' = 25t - \frac{1}{2} 	imes 9.8 	imes t^2$$s' = 25t - 4.9t^2$ ............. $(2)$The sum of the displacements of both stones at the meeting point is equal to the total height of the tower,$100\, m$:$s + s' = 100$$4.9t^2 + 25t - 4.9t^2 = 100$$25t = 100$$t = 4\, s$In $4\, s$,the distance covered by the falling stone from the top is:$s = 4.9 	imes (4)^2 = 4.9 	imes 16 = 78.4\, m$.Therefore,the stones will meet after $4\, s$ at a height of $(100 - 78.4) = 20.6\, m$ from the ground.

$A$ stone is allowed to fall from the top of a tower $100\, m$ high and at the same time another stone is projected vertically upwards from the ground with a velocity of $25\, m/s$. Calculate when and where the two stones will meet.

Similar Questions

Gravitational force on the surface of the moon is only $\frac{1}{6}$ as strong as the gravitational force on the earth. What is the weight in newtons of a $10\, kg$ object on the moon and on the earth?

What do we call the gravitational force between the earth and an object?

Amit buys a few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not,why? [Hint: The value of $g$ is greater at the poles than at the equator.]

The volume of a $500\, g$ sealed packet is $350\, cm^3$. Will the packet float or sink in water if the density of water is $1\, g\, cm^{-3}$? What will be the mass of the water displaced by this packet?

How does the gravitational force $(F)$ between two objects change when the distance between them is reduced to half?

Vedclass Test Series

Exam Paper Generator

Online Exam Module