In Example 7.7, we found that the speed of a roller coaster that had descended 20.0 m was only slightly greater when it had an initial speed of 5.00 m/s than when it started from rest. This implies that ??PE >> KE?i . Confirm this statement by taking the ratio of ??PE to KE?i . (Note that mass cancels.) Example 7.7 Finding the Speed of a Roller Coaster from its Height (a) What is the final speed of the roller coaster shown in ?Figure 7.8 ?if it starts from rest at the top of the 20.0 m hill and work done by frictional forces is negligible? (b) What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?

Step-by-step solution 19PE Step 1 of 3 The expression to find the initial kinetic energy is given below, Here, m is mass and is velocity. The change in potential energy is equal to the product of mass, acceleration due to gravity and height, hence potential energy is, Step 2 of 3 Take the ratio of change in potential energy to initial kinetic energy, Mass gets cancelled, Substitute for , 20 m for h and 5 m/s for solve for ratio, Therefore,