Conservation of Energy Help (p2)

[kissafilipino]

Homework Statement

From what height would a compact car have to be dropped to have the same kinetic energy that it has when being driven at 105 km/h? Unless otherwise directed, assume that air resistance is negligible.

Answer: __ m
Velocity: 105 km/h -> 105000 m/s

Height: ?

Homework Equations

Conservation of energy equation: (thanks to user MillerGenuine)
U= potential energy
K= kinetic energy
Conservation of
energy => Kf + Uf = Ki + Ui

K = 1/2mv^2
U = mg(delta h)

The Attempt at a Solution

My attempt was somewhat he same trying to input in the equation, what height = the same kinetic energy of 115 k/m. So I said, gravitational potential energy = kinetic energy
U = K
mg(delta h) = (1/2)mv^2
Since mass is in both sides, it can be taken out.
g(delta h) = (1/2)v^2
(9.81)(delta h) = (1/2)105000^2
(9.81)(delta h) = (1/2)11025000000
(9.81)(delta h) = 5512500000
delta h = 561926605 m?

 

[Pengwuino]

Keep your units straight. Kilometers/hour is not SI units.

 

[kissafilipino]

Exactly, that I understood, which is why I changed it from Km to meters
105 km/h -> 105000 m/s and used it in the equation: mg(delta h) = (1/2)mv^2

 

[Pengwuino]

You changed km -> m but didn't correctly change hours -> seconds. 105km/h is about the speed a car is driven. Does your speed sound reasonable?

 

[rwisz]

Your attempt at solving the problem is correct. The height at which the compact car should be dropped to have the same kinetic energy as when it is being driven at 105 km/h is approximately 561926605 meters. This calculation is based on the conservation of energy principle, which states that the total energy of a system remains constant. In this case, the initial potential energy of the car at the top of the drop is converted into kinetic energy as it falls. Neglecting air resistance, the car would have the same kinetic energy at the bottom of the drop as it does when being driven at 105 km/h. It is important to note that this is a theoretical calculation and in reality, the car would experience air resistance and other factors that would affect its final velocity and kinetic energy.