An item is being lifted by an elevator at a constant speed to a height of 10 feet. The item does not move for five seconds then catapults off the 10-foot platform and back to the ground. Compare the height of the item to the time passed in seconds. Determine the correct types of functions that describes the scenario in the correct order.

Question

Responses

Linear Function, Constant Function, Quadratic Function

Linear Function, Constant Function, Linear Function

Quadratic Function, Constant Function, Linear Function

Constant Function, Quadratic Function, Linear Function

Answer 1

To analyze the scenario, we can break it down into different segments based on the motion described:

1. Lifting the item at constant speed to a height of 10 feet: While the item is being lifted, its height increases linearly over time. So, this part can be described by a linear function.

2. Item does not move for five seconds: After reaching the 10 feet height, the item remains at this height for a period of time. This is a constant function since the height remains the same regardless of time.

3. Item catapults off the platform back to the ground: Once the item is released, it will follow a projectile motion, resulting in a trajectory that can be described by a quadratic function as the height changes over time in a parabolic manner until it reaches the ground.

Putting it all together, we can sequence the types of functions corresponding to the time segments of the scenario:

1. Linear Function (lifting the item)
2. Constant Function (item stationary)
3. Quadratic Function (item falling back to the ground)

The correct order is:

Linear Function, Constant Function, Quadratic Function.