# The cyclist, having developed a speed of 54 km / h, tries to accelerate

**The cyclist, having developed a speed of 54 km / h, tries to accelerate (without pedaling) a mountain 10 m high. Determine if he can do it. Disregard friction.**

Given:

Cyclist speed v = 54 km / h = 54000m / 3600s = 15m / s.

The height of the mountain is h = 10 m.

g = 9.8 m / s ^ 2.

Solution:

This problem can be solved using the law of conservation of energy.

At the bottom of the trajectory, the cyclist has kinetic energy Ek = (mv ^ 2) / 2.

As it rises, it transforms into potential energy Ep = mgh,

where m is the mass of a cyclist with a bicycle, g is the acceleration of gravity.

To answer the question of the problem, you need to find out whether the inequality holds:

Ek> Ep;

(mv ^ 2) / 2> mgh;

mv ^ 2> 2 * mgh;

v ^ 2> 2gh;

15 ^ 2 [m ^ 2 / s ^ 2]> 2 * 9.8 * 10 [m ^ 2 / s ^ 2];

225> 196.

We see that the inequality is satisfied. This means that the reserve of kinetic energy is enough for a cyclist to climb a mountain 10 m high.

Answer: Yes, a cyclist can ride up a 10 m high mountain without pedaling.