Question

A stone is thrown vertically upward direction with a velocity of 40m/s at what height kinetic energy equals to potential energy

Answer 1

Hello there!

The types of energy related with motion are Kinetic Energy and Potential Energy. Potential Energy is the amount of energy when the object is not moving, and Kinetic Energy is the amount of energy when the object is moving.

In this case, they are asking the moment when the P.E is equal to K.E. To solve this, we have to keep in mind that Kinetic Energy = Potential Energy. Now write the formulas of both of them, and let's start solving!

⇒ $K.E = P.E$

⇒ $\frac{1}{2}mv^{2} = mgh$

We can cancel the $m$ from both sides.

⇒ $\frac{1}{2}v^{2} = gh$

It is given that $v=40 \frac{m}{s}$

⇒ $\frac{1}{2}\times40^{2} = gh$

⇒ $\frac{1600}{2} = gh$

⇒ $800 = gh$

Let us assume that $g=10 \frac{m}{s^{2}}$

⇒ $800 = 10h$

⇒ $h = \frac{800}{10} = 80$ meters

That's it! This is how you can solve this problem.

Important points/concepts to remember:

1. Formulas of Kinetic and Potential Energy
2. Find the relation between them (in this case, they are equal, as mentioned by the question)
3. Appropriately cancel terms which are on both sides
4. Substitute the values of variables, if they are given in the question.