A roller coaster car drops a maximum vertical distance of 35.4 m. Part A Determine the maximum speed of the car at the bottom of that drop. Ignore work done by friction. Express your answer with the appropriate units.

26.34 m/s.

Explanation:

Given:

h = 5.4 m

g = 9.81 m/s^2

Change in Potential energy = change in Kinetic energy

mgh = 1/2mv²

gh = 1/2 v²

v = √2gh

= √2*9.8*35.4

=√693.84

v = 26.34 m/s.

Maximum vertical distance or height = h = 35.4 m

let's consider the initial speed at the top is zero.

As the roller coaster is coming from top to bottom there is the conversion of gravitational potential energy into kinetic energy. So we will consider the law of conservation of energy.

As in this case,

Loss in potential energy = Gain in Kinetic energy

mgh = 1/2mv²

mass will cancel out will mass.

gh = 1/2 v²

v = √2gh

v = √2*9.8*35.4

v = √693.84

v = 26.34 m/s

The rollar coaster will have the maximum speed of 26.34 m/s when it reaches the bottom if we ignore the frictional forces.