Question

In Kingda Ka roller coaster starts with a speed of 6 m/s at the top of the drop and attains a speed of 50.3 m/s when it reaches the bottom. If the roller coaster were then to start up an identical hill, what speed would it attain when it reached the top? Assume that friction and air resistance are absent. EXACTLY 6 m/sWhy is the answer 6?

Answer 1

Explanation:

According to the law of conservation of energy,

          $P.E_{i} + K.E_{i} = P.E_{f} + K.E_{f}$  ......... (1)

As we know that,  P.E = mgh

and,     K.E = $\frac{1}{2}mv^{2}$

Therefore, putting these values of P.E and K.E into equation (1) as follows.

        $mgh + m \frac{(6)^2}{2} = 0 + m \frac{(50.3)^2}{2}$

Now, initial case is that its starts with 50.3 m/s at bottom.

          P.E = m  and PE = 0

And, as it reaches the height h,

       P.E = mgh

So,        K.E will be m

Hence, speed = 6 m/s