Question

A stone is thrown vertically upward with a velocity of $19.6m/s$. After 2 seconds, another stone is thrown upwards with a velocity of $9.8m/s$. When and where will these stones collide?

Answer 1

Hint In this case, 2 stones are thrown with a gap of 2 seconds between them. Initially calculate the distance travelled by the first stone thrown with above specified velocity . After 2seconds, the second stone is thrown up and will be afloat till the third second. Compare the relative acceleration of the second stone with the first one and find the height where they actually meet.

Complete Step By Step Solution
When stone 1 is thrown up with an initial velocity of $19.6m/s$, the final velocity of the ball after2 seconds is given by the motion equation,
$v = u + at$,where v is the final velocity of the stone after 2 seconds.
$\Rightarrow v = 19.6 + ( - 9.8) \times 2$ (Since when the stone is thrown up, acceleration is due to the downward gravitational force)
$\Rightarrow v = 0m/s$
So , the maximum height that stone one can reach can be identified using second equation of motion,
$s = ut + \dfrac{1}{2}g{t^2}$, where s is the maximum height the stone can reach.
$\Rightarrow s = (19.6 \times 2) + \dfrac{1}{2}( - 9.8 \times 4)$
$\Rightarrow s = 19.6m$
Thus stone 1 can reach a maximum height of 19.6 meters in 2 seconds from ground when thrown at$19.6m/s$. In order for the second stone to reach the first stone at 19.6 meters, when it is thrown at $9.8m/s$, it will take another 2 seconds to reach the point of maximum height.
If a stone to reach a point against gravity takes a time period, then the time period for it to come back to its normal position will also be the same. Hence, stone 1 will take 2 seconds to drop ground from 19.6 meters. As stone 1 starts to move towards ground, stone 2 starts its acceleration . Thus when stone 2 is at 19.6 meters, stone 1 will land on the ground and hence stone 2 after a period of 4 seconds. Thus both the stones will meet on the ground after a period of 4 seconds.

Note When an object is thrown up from ground, the object is said to be thrown against gravitational force, and thus will travel a limited distance and get pulled back. This will have a negative g value. But, when a stone is dropped from a certain height, it moves along with gravitational forces and thus will have positive g value.