Question

An NCC parade is going at a uniform speed of 6 km/h through a place under a berry tree on which a bird is sitting at a height of 12.1m. At a particular instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on his uniform?

Answer 1

Use distance formula in the chapter of Rest and Motion we can say kinematics formulas. Substituting all the given values in the formula we get time. By using this time value we get distance value with the help of using speed which is given in the question.

Formula used:
$S=ut+\dfrac{1}{2}a{t^2}$

Complete answer:
First we have to write given values mentioned in the question.
Initial velocity= 0 m/s
a= 9.8 m/s2
Distance=S = 12.1 m
Let t be the true time of fall
$S = ut + \dfrac{1}{2}a{t^2}$
S is the distance
u is the initial velocity
t is the time
a is the acceleration.
Put given values in the formula
$\Rightarrow 12.1 = 0 + \dfrac{1}{2} \times 9.8 \times {t^2}$
\eqalign{ & \Rightarrow {t^2} = \dfrac{{12.1}}{{4.9}} \cr & \Rightarrow {t^2} = 2.46\sec \cr & \therefore t = 1.57\sec \cr}
Given velocity 6km/h is converted into m\s so we have
Velocity=6km/h
$\Rightarrow velocity = \dfrac{{6 \times 5}}{{18}}$
$\therefore 1.66m/\sec$
We know that formula
Distance = Speed x time
\eqalign{ & {\text{distance}} = 1.57 \times 1.66 \cr & \therefore {\text{distance = 2}}{\text{.6m}} \cr}

Therefore 2.6m away from the tree will receive the berry on his uniform.

Additional information:
$\bullet$ We have to know velocity is equivalent to a specification of an object's speed and direction of motion. Its SI unit is m/sec.
$\bullet$ Acceleration is a vector quantity as it has both magnitude and direction, acceleration is defined as the rate of change of velocity with respect to time. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time.
$\bullet$ Motion is the state of change in position of an object over time. It is described in terms of displacement, distance, velocity, acceleration, time and speed. Hence there are three equations of motion to use finding these terms.

Note:
In this type of question, we have to clearly understand the question because using very simple formulas we can solve these problems. We can see here velocity is a physical vector quantity it is nothing but speed, velocity is a fundamental concept in kinematics.