Calculating Final Velocity of a Car Rolling into a Station

[albert611]

Hi, I attempted this problem, but I do not see how it makes sense. Could somebody give me an idea of how to solve this problem? Thanks!

While traveling along at 24.3 m/s, a 13.7 kg car runs out of gas 16 km from a service station. Neglecting friction, if the station is on a level 14.8 m above the elevation of the car, how fast will the car be going when it rolls into the station?

The correct answer should be 17.33 m/s BTW.

Thank you very much for your help!

-Albert

 

[Zlex]

Well, let's see.

Find the component of gravity that is slowing down the car. That'll be your negative acceleration. You have all the other information. Use the appropriate kinematic equation, plug and chug.

 

[aviv87]

Also, if you know how to calculate potential gravitational energy and kinetic energy you could use the energy conservation law.

 

[HallsofIvy]

In other words:
1) find the kinetic energy of the car using E_k= (1/2)mv².
2) find the increase in potential energy as the car moves up to the gas station using
E_p= mgh.
3) find the kinetic energy of the car at the gas station assuming conservation of energy
4) find the speed of the car from the kinetic energy using, again E_k= (1/2)mv².

 

[Tom McCurdy]

I would advise setting up the problem as follows
$$KE_i+U+i=KE_f+U_f$$
KE=Kinetic Energy
U=Potential Energy
KE=1/2 m v^2
U=mgy

We can assume the $$U_f$$ will go to zero

$$1/2mv^2 = 1/2mx^2 + mgy$$ solving for x

the m's cancel out

$$1/2 v^2 = 1/2 x^2 + gh$$

solve for x and volla 17.3323


so end the end you did not need to know the cars mass or the 16 miles... go conservation of energy

 

[tony873004]

A 13.7 kg car? It'll be blown away by the wind before it gets there!