How Fast Will the Roller Coaster Car Be at the Top of the Loop?

[NkaujHelp]

Homework Statement

At one point in a roller-coaster, a single 300 kg car goes around a vertical, circular loop with a diameter of 24 m. It enters the loop at the bottom with a speed of 20 m/s. What will its speed be at the top?

Homework Equations

Kinetic Energy = 1/2mv^2
Gravitational Energy = mgh

The Attempt at a Solution

Initial Energy = Final Energy => Kinetic Energy of the Bottom = Kinetic Energy of the Top + Gravitational Energy at the Top

I set up the equation for this problem and plugged in numbers to solve this, but I have a negative answer under the square root. Am I missing something else here?

 

[ehild]

You are right, that car will not reach the top.

 

[Simon Bridge]

To check - and help you understand your result - ask instead: "does the car have enough initial kinetic energy to get to the top?"
Or, another way, what is the highest the car can reach?