Question

Select the correct answer from each drop-down menu.

A roller coaster moves along an inclined linear path before it reaches its maximum height. The car moves at a constant speed and gains 4 meters in height every 3 seconds.

The slope of the line that represents the height of the car in meters in terms of time in seconds is ___

Pick answer for seconds:
3/5
4/5
4/3
5/3

If the car takes 54 seconds to reach the maximum height, then the maximum height above the ground is __ meters.

Pick answer for Meters;
54
72
81
90

Answer 1

The slope of the height over time for the roller coaster is 4/3, and the maximum height reached after 54 seconds is 72 meters.

Step-by-step explanation:

The slope of the line representing the height of the car in terms of time is calculated by the change in height over the change in time. For this roller coaster car, it gains 4 meters in height every 3 seconds, so the slope is 4 meters/3 seconds or 4/3.

To determine the maximum height after 54 seconds, we multiply the rate of ascent by time. The car ascends 4 meters every 3 seconds, so in 54 seconds it will ascend 54/3 = 18 times 4 meters, giving us 72 meters as the maximum height.

Answer 2

The slope of the line representing the height of the car as a function of time is 4/3, and the maximum height the car reaches after 54 seconds is 72 meters.

Step-by-step explanation:

The slope of the line that represents the height of the car in meters in terms of time in seconds is the change in height divided by the change in time. In this case, the height changes by 4 meters every 3 seconds, so the slope is 4/3.

If the car takes 54 seconds to reach the maximum height, to find the maximum height above the ground, we multiply the rate of height gain (4 meters every 3 seconds) by the total time (54 seconds). That calculation looks like this: (4 meters / 3 seconds) x 54 seconds = 72 meters.