Answer to Question #165222 in Physics for zayed

Question

A car, starting from rest at position X, accelerates up a hill. The car reaches a speed of 10m / s at position Y. The kinetic energy of the car at position Y is equal to its gain in gravitational potential energy from X to Y. X Y gain in height of car Take the gravitational field strength g to be 10N/ kg. What is the gain in height of the car between X and Y?

Answer 1

The kinetic energy of the car at position Y is the following:

$$K = \dfrac{mv^2}{2}$$

where $m$ is the mass of the car, and $v = 10 m/s$ is its speed. The gravitational potential energy from X to Y, which is given as follows:

$$U = mgh$$

where $g = 10 N/kg$ is the gravitational accleration, and $h$ is the gain in height of the car between X and Y.

Since these two quantities are equal, obtain:

$$\dfrac{mv^2}{2} = mgh\\ h = \dfrac{v^2}{2g}\\ h = \dfrac{10^2}{2\cdot 10} = 5 m$$

Answer. 5 m.