Question

STT 10.7 At a water park, katie slides down each of the frictionless slides shown. At the top, she is given a push so that she has the same initial speed each time. At the bottom of which slide is she moving the fastest?

A Slide A B Slide B
C slide C D her speed is the same at the bottom of all three slides

Answer 1

Katie will be moving the fastest at the bottom of Slide C.

Step-by-step explanation:

The speed of an object at the bottom of a slide is determined by its potential energy at the top, converted to kinetic energy at the bottom. The law of conservation of energy states that energy is conserved, so the initial potential energy is converted into kinetic energy. The kinetic energy (KE) is given by the formula \(KE = mgh\), where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

Comparing the three slides, the slide with the greatest vertical height will result in the highest speed at the bottom. Therefore, Katie will be moving the fastest at the bottom of Slide C since it has the greatest vertical drop.

In conclusion, the key factor in determining the speed at the bottom of each slide is the vertical height. As Slide C has the greatest height among the three slides, Katie's speed at the bottom will be the fastest when she descends down Slide C.