Jasmine launches a model rocket from a cliff. The rocket goes up 16.8 feet above the cliff, then it drops 28.1 feet into the ocean below. Complete the statements to describe how to determine the change in height from the cliff to the ocean below. Click the arrows to choose an answer from each menu. The change in height between the launch point on the cliff and the distance above the cliff that the rocket reaches is best represented by a Choose… number. The change in height from the top height of the rocket to the ocean below the cliff is best represented by a Choose… number. The expression Choose… best represents the change in height from the cliff to the ocean below. The change in height from the cliff to the ocean below is Choose… feet.
The Correct Answer and Explanation is:
Correct Answers:
- The change in height between the launch point on the cliff and the distance above the cliff that the rocket reaches is best represented by a
➡️ positive number. - The change in height from the top height of the rocket to the ocean below the cliff is best represented by a
➡️ negative number. - The expression
➡️ +16.8 − 28.1
best represents the change in height from the cliff to the ocean below. - The change in height from the cliff to the ocean below is
➡️ −11.3 feet.
Explanation
To determine the total change in height from the launch point on the cliff to the ocean below, we need to track the rocket’s vertical movement in two phases:
- Ascent: The rocket first rises 16.8 feet above the cliff. This is an upward movement, which is represented by a positive number. So, the change in height here is +16.8 feet.
- Descent: Then, the rocket falls from its highest point (which is 16.8 feet above the cliff) down to the ocean, which is 28.1 feet below the cliff. This is a downward movement, and it includes both the 16.8 feet it rose and an additional distance below the cliff. Since this is a downward change in position, it is represented by a negative number, specifically −28.1 feet.
To find the net change in height from the cliff (launch point) to the ocean (final point), we combine these two changes using this expression:
Change = +16.8 − 28.1
Now we perform the calculation:
+16.8 − 28.1 = −11.3 feet
This result means the rocket ends up 11.3 feet below the level of the cliff.
In summary, even though the rocket initially ascended, its final position relative to the launch point is lower. The net change is negative, indicating a drop in height of 11.3 feet from the cliff to the ocean.
