Name: Inertial Frames of Reference
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: Imagine if you are on a bus or a train, can you say you are in an inertial frame of reference? If yes, how can you predict it? Let us explore more in this vi...

Question

From the top of a tower, a stone is thrown vertically upward with a velocity of

30 {ms}^{- 1}

and

4

seconds later another stone is dropped from the same point. Both the stones reach the ground at the same time. Find the height of the tower and the time of fall of the second stone.(

g = 10 {ms}^{- 2}

.)

Accepted Answer

Given, the vertical velocity of the stone = $30 m / s$ .

Let time taken by second stone be $g = 10 {ms}^{- 2}$ seconds. Then, time taken by first stone will be $(t + 4)$ seconds.

Let downward direction be taken positive.

For second stone, applying second equation of motion, $s = u t + \frac{1}{2} a t^{2}$ .

$h = (0) t + \frac{1}{2} {gt}^{2} or h = 5 t^{2}$ ..................................(1)

For first stone, we can break the path in two parts. One is upward motion and second is downward motion from the highest point.

For upward motion, applying first equation of motion, $v = u + a t$ .

$0 = 30 - 10 t \Rightarrow t = 3 s$

Distance in upward direction can be found using second equation of motion, $s = u t + \frac{1}{2} a t^{2}$

$x = 30 \times 3 - \frac{1}{2} \times 10 \times 3^{2} = 45 m$

For downward motion, initial velocity $= 0$ , total distance $= h + 45$ ,

Time $= t + 4 - 3 = t + 1$ seconds.

Applying second equation of motion,

$h + 45 = (0) (t + 1) + \frac{1}{2} \times 10 \times {(t + 1)}^{2} \Rightarrow h + 45 = 5 {(t + 1)}^{2}$ ..(2)

From equation (1) and (2),

$5 t^{2} + 45 = 5 {(t + 1)}^{2} \Rightarrow t^{2} + 9 = t^{2} + 2 t + 1 \Rightarrow 9 = 2 t + 1$

Or $t = 4 \sec .$

Substituting in (1),

$h = 5 {(4)}^{2} = 80 m$ .

Hence, height of tower is $80 m$ and time of fall of second stone is $4$ seconds.

Important Questions on Motion of a Particle

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From the top of a tower, a stone is thrown vertically upward with a velocity of 30 ms-1 and 4 seconds later another stone is dropped from the same point. Both the stones reach the ground at the same time. Find the height of the tower and the time of fall of the second stone.(g=10 ms-2.)

Important Questions on Motion of a Particle

Learn and Prepare for any exam you want !