Name: Equations of Motion Using Graphs
Uploaded: 2019-07-19
Duration: 9 min 14 s
Description: Equations of motion help us solve numerous problems and predictions related to motion. Let us understand their derivation using graphs in this video.

Question

Two stones are thrown vertically upwards simultaneously with their initial velocities

u_{1}

and

u_{2}

respectively. Prove that the heights reached by them would be in the ratio of

{u_{1}}^{2} : {u_{2}}^{2}

(Assume upward acceleration is

- g

and downward acceleration to be

+ g

).

Accepted Answer

At the highest point, final velocity will become zero, $v = 0$

For the stone thrown with velocity $u_{1}$ ,

$0 - u_{1}^{2} = 2 (- g) h_{1} (∵ v^{2} - u^{2} = 2 a s)$

or $h_{1} = \frac{u_{1}^{2}}{2 g}$

Similarly, for the stone thrown with velocity $u_{2}$ ,

$h_{2} = \frac{u_{1}^{2}}{2 g},$

$∴$ The required ratio, $\frac{h_{1}}{h_{2}} = \frac{u_{1}^{2}}{2 g} \times \frac{2 g}{u_{2}^{2}} = \frac{u_{1}^{2}}{u_{2}^{2}} .$

Or $h_{1} : h_{2} = u_{1}^{2} : u_{2}^{2}$ .
So, the heights reached by them would be in the ratio of ${u_{1}}^{2} : {u_{2}}^{2}$ .

Two stones are thrown vertically upwards simultaneously with their initial velocities $u_{1}$ and $u_{2}$ respectively. Prove that the heights reached by them would be in the ratio of ${u_{1}}^{2} : {u_{2}}^{2}$ (Assume upward acceleration is $- g$ and downward acceleration to be $+ g$ ).

Important Questions on Motion

Learn and Prepare for any exam you want !

Two stones are thrown vertically upwards simultaneously with their initial velocities u1 and u2 respectively. Prove that the heights reached by them would be in the ratio of u12:u22 (Assume upward acceleration is -g and downward acceleration to be +g).

Important Questions on Motion

Learn and Prepare for any exam you want !

Two stones are thrown vertically upwards simultaneously with their initial velocities $u_{1}$ and $u_{2}$ respectively. Prove that the heights reached by them would be in the ratio of ${u_{1}}^{2} : {u_{2}}^{2}$ (Assume upward acceleration is $- g$ and downward acceleration to be $+ g$ ).