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

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

The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

Calculate the force of gravitation between the Earth and the Sun,given that the mass of the Earth $= 6 \times 10^{24} \, kg$ and of the Sun $= 2 \times 10^{30} \, kg$. The average distance between the two is $1.5 \times 10^{11} \, m$.

What do you mean by acceleration due to gravity?

Why is it difficult to hold a school bag having a strap made of a thin and strong string?

Vedclass Test Series

Exam Paper Generator

Online Exam Module