If a stone is projected vertically upward from the ground with a speed of \(10~\text{m/s}\), then its:
(take \(g=10\) m/s2)
Hint: Potential energy is maximum at the highest point.
Step 1: Find the time taken to reach the maximum height.
\(v=u+at\\ 0=10-10t\\ t=1~\text{s}\)
Therefore, the potential energy will be maximum at \(t=1~\text{s}\)
Step 2: Find height where kinetic energy is equal to potential energy
\(v^2=u^2-2gh \dots(1)\\ K.E=P.E\\ \frac{1}{2}mv^2=mgh\\ \text{From equation (1)}\\ u^2-2gh=2gh\\ \Rightarrow u^2=4gh\\ \Rightarrow h=\frac{u^2}{4g}\\ \Rightarrow h= 2.5~\text{m} ~~~~\left[u= 10~\text{m/s}, g = 10 ~\text{m/s}^2\right]\)
Therefore, kinetic energy is equal to the potential energy at a height of \(2.5~\text{m}\) from the ground.
Hence, option (3) is the correct answer.