A truck, initially at rest, rolls down a frictionless hill and attains a speed of 20 m/s at the bottom. To achieve a speed of 40 m/s at the bottom, how many times higher must the hill be

To achieve the velocity of 40 m/sec height will become 4 times  

Explanation:

We have given initially truck is at rest and attains a speed of 20 m/sec

Let the mass of the truck is m

At the top of the hill potential energy is mgh and kinetic energy is

So total energy at the top of the hill

At the bottom of the hill kinetic energy is equal to and potential energy will be 0

So total energy at the bottom of the hill is equal to

Form energy conservation

, for v = 20 m/sec

Squaring both side

h = 20.408 m

Now if velocity is 0 m/sec

h = 81.63 m

So we can see that to achieve the velocity of 40 m/sec height will become 4 times

no. bullets are macro objects. wave nature is for light waves, extremely tiny particles. if a light particle was the size of your finger, the bullet would be the size of the universe. so basically, that huge difference in size makes the wave nature of matter insignificant.