Question

An Object is thrown vertically upwards with velocity of 20 m/s. At what height will its kinetic energy and potential energy be equal ? $(g=10m/s^2)$

• A. $10m$
• B. $20m$
• C. $15m$
• D. $5m$

Answer 1

The correct option is A $10m$

In this question Kinetic energy is converting to potential energy
Initial velocity u = 20 m/s


$H_{max}=\frac{u^2}{2g}=\frac{20\times 20}{2\times 10}{H}_{max}=20m\text{So, at 20m the K.E. will entirely}\text{change into P.E.}\text{Hence, at the height of 10m.}\text{K.E. of the object will be equal to}\text{its P.E.}P.E.=mghK.E.=\frac{1}{2}m{v}^{2}mgh=\frac{1}{2}m{v}^{2}gh=\frac{1}{2}{v}^{2}gh=\frac{1}{2}(u^2-2gh)(v^2=u^2+2as{v}^2=u^2-2gh)gh=\frac{u^2}{2}-gh2gh=\frac{u^2}{2}h=\frac{u^2}{4g}=\frac{20\times 20}{4\times 10}h=10m$