Question

A ball of mass m is dropped from
height h. Which among the following
will represent the motion of ball?​

Answer 1

Given:

A ball of mass m is dropped from height h.

To find:

Which "displacement-time graph" represents the motion of the ball ?

Calculation:

Since the ball is dropped, its initial velocity is zero.

Considering downward direction to be positive, we can say that :

2nd equation of kinematics:

$\sf \: h = ut + \dfrac{1}{2} a {t}^{2}$

$\sf \: \implies h = (0)t + \dfrac{1}{2} g {t}^{2}$

$\sf \: \implies h = \dfrac{1}{2} g {t}^{2}$

Since g is constant , we can say :

$\sf \: \implies h \propto {t}^{2}$

So, the graph will be :

$\setlength{\unitlength}{2.5mm}\begin{picture}(10,10)\linethickness{0.45mm}\put(20,20){\vector(1,0){18}}\put(37,19){t}\put(20,20){\vector(-1,0){18}}\put(20,20){\vector(0,1){18}}\put(19,37){s}\put(20,20){\vector(0,-1){18}}\multiput(19.35,6)(0,2){15}{\line(1,0){1.3}}\multiput(6,19.35)(2,0){15}{\line(0,1){1.3}}\put(20,20){\circle*{1}}\qbezier(20,20)(25,21)(27,36)\end{picture}$

Hence, a parabolic curve will be obtained to represent this motion.