Question

A stone is dropped from a rising balloon at a height of $76{\text{ m}}$ above the ground and reached the ground in $6{\text{ s}}$. What was the velocity of the balloon when the stone was dropped? Take $g = 10{\text{ m}}{{\text{s}}^{ - 2}}$.
A. $\dfrac{{52}}{3}{\text{ m}}{{\text{s}}^{ - 1}}$ upward
B. $\dfrac{{52}}{3}{\text{ m}}{{\text{s}}^{ - 1}}$ downward
C. $3{\text{ m}}{{\text{s}}^{ - 1}}$
D. $9.8{\text{ m}}{{\text{s}}^{ - 1}}$

Answer 1

Hint:In this question, we are given the height, time, and acceleration due to gravity. We have to find the velocity of the balloon. Apply the direct formula $s = ut - \dfrac{1}{2}a{t^2}$ where $a = g$. Also, take the distance to be negative as the stone dropped in downward direction. If the velocity will be negative, it means it is in downward direction. If positive, it means upward direction.


Formula used:

Second equation of the motion $s = ut - \dfrac{1}{2}a{t^2}$ where $a = g$


Complete answer:
Equation of motion: These are the mathematical equations used to estimate the end velocity, displacements, duration, and so on of a moving object without taking into account the force acting on it. These equations are only applicable when the body's acceleration is constant, and it moves in a straight line.
There are three equations of the motion i.e., $v = u + at$, $s = ut + \dfrac{1}{2}a{t^2}$, ${v^2} = {u^2} + 2as$
Given that,
Height $s = - 76{\text{ m}}$ (stone was dropped in downward direction)
Acceleration due to gravity $g = 10{\text{ m}}{{\text{s}}^{ - 2}}$
Time $t = 6{\text{ s}}$
Now, applying the second equation of the motion i.e., $s = ut - \dfrac{1}{2}a{t^2}$ where $a = g$
Here, the stone was dropped in the downward direction and the gravitational force is in downward direction. So, we are applying $s = ut - \dfrac{1}{2}a{t^2}$. If the object is moving in upward direction and the acceleration will be given then apply $s = ut + \dfrac{1}{2}a{t^2}$.
Substitution all the required values,
We get,
$ - 76 = 6u - \dfrac{1}{2}\left( {10} \right){\left( 6 \right)^2}$
$ - 76 = 6u - 180$
On solving, it will be $u = \dfrac{{52}}{3}{\text{ m}}{{\text{s}}^{ - 1}}$ (upward direction).
Hence, option (A) is the correct answer i.e., $\dfrac{{52}}{3}{\text{ m}}{{\text{s}}^{ - 1}}$ upward.







Note:In physics, motion is the change in position or orientation of a body over time. Translation is movement along a straight line or a curve. Rotation is defined as motion that alters the orientation of a body. All places in the body have the same velocity (directed speed) and acceleration in both circumstances (time rate of change of velocity). The most common type of motion involves translation and rotation. Every movement is relative to some frame of reference. Saying that a body is at rest, or that it is not in motion, simply indicates that it is being described in relation to a frame of reference that is moving together with the body.