the speed of a roller coaster that had descended 29.0 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 ΔPE KEi. Confirm this statement by taking the ratio of ΔPE to KEi. (Note that mass cancels.)
To confirm the statement, we need to calculate the ratio of the change in potential energy (ΔPE) to the initial kinetic energy (KEi).
The potential energy can be calculated using the formula:
PE = m * g * h
Where:
m is the mass of the roller coaster
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the change in height (29.0 m in this case)
Since the problem states that the mass cancels, we can assume that the mass of the roller coaster is constant.
The initial kinetic energy (KEi) can be calculated using the formula:
KEi = 0.5 * m * v^2
Where:
m is the mass of the roller coaster
v is the initial velocity (5.00 m/s in this case)
Now, let's calculate the ratio of ΔPE to KEi.
Step 1: Calculate ΔPE
ΔPE = (m * g * h) - 0
Step 2: Calculate KEi
KEi = 0.5 * m * v^2
Step 3: Calculate the ratio
Ratio = ΔPE / KEi
Since we know mass cancels out, we don't need to consider it in the ratio calculation.
By comparing the values of ΔPE and KEi, we can see if ΔPE is slightly greater than KEi as stated in the problem.