Home
Class 11
PHYSICS
A stone is allowed to fall from the top ...

A stone is allowed to fall from the top of a tower 300 m height and at the same time another stone is projected vertically up from the ground with a velocity `100 ms^(-1)` . Find when and where the two stones meet ?

Text Solution

Verified by Experts

Let the two stones meet at C. The tiem of travel of the stones are equal . Vertically projected body travels a distance of x, while the freely falling body travels a distance of `(h-x)`.
For the stone moving upwards
`u=100ms^(-1), a =-9.8ms^(-1), t=?, s=x`
From the equation `s=ut+1/2at^(2), x=100t-1/2xx9.8t^(2)`
`x=100t-4.9t^(2)` ....(1)
For freely falling body
`u=0,a=9.8ms^(-2)`
`t=? s=h -x=(300-x)`
From eq.s =`ut+1/2xx9.8t^(2)`
`(300-x)=0+1/2xx9.8t^(2) (300-x)=4.9t^(2)` ......(2)
Adding equation (1)and(2)
`300=100trArrt=3sec`
substitute this value in equation (10
`x=100xx3-4.9xx9=300-44.1=255.9m`
the two stones meet after 3 sec and at a height of `255.9` from the ground.
Promotional Banner

Similar Questions

Explore conceptually related problems

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

A stone is dropped from a height 300 m and at the same time another stone is projected vertically upwards with a velocity of 100m//sec . Find when and where the two stones meet.

A stone is dropped from a tower of height 200 m and at the same time another stone is projected vertically up at 50 m/s. The height at which they meet ? [g=10 "m/s"^2]

One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of distance (s) between the two stones varies with time (t) as (before either stone hits the ground).

A stone is dropped from the top of a tower of height h=60m. Simultaneously another stone is projected vertically upwards from the foot of the tower. They meet at a height (2h)/3 from the ground level. The initial velocity of the stone projected upwards is (g=10ms^(-2))

A stone is dropped from the top of a tower. If it hits the ground after 10 seconds, what is the height of the tower?

A stone is dropped from the top of a tower and one second later, a second stone is thrown vertically downward with a velocity 20 ms^-1 . The second stone will overtake the first after travelling a distance of (g=10 ms^-2)

A stone dropped from the top of a tower reaches the ground in 3 s. The height of the tower is

A target is fixed on the top of a tower 13 m high. A person standing at a distance of 50 m from the pole is capable of projecting a stone with a velocity 10 sqrt(g) ms^-1 . If he wants to strike the target in shortest possible time, at what angle should he project the stone ?

A stone is dropped from the top of a tall cliff and n seconds later another stone is thrown vertically downwards with a velocity u . Then the second stone overtakes the first, below the top of the cliff at a distance given by