A hot air balloon pilot raises a balloon 200 m from the ground, turns off the burner, and allows the balloon to descend 60 m before turning the burner on again to raise it another 170 m.
a. Use positive and negative values to represent each stage of the balloon’s flight path.
b. Use absolute values to determine the total vertical distance travelled by the balloon.
Height has magnitude AND DIRECTION (up if +, down if -)
It is a VECTOR
distance has only magnitude. It has no direction. We call it a SCALAR.
Use dictionary for those.
a. Using positive (+) and negative (-) values to represent each stage of the balloon's flight path:
1. As the balloon is raised 200 m from the ground, we can represent this as a positive value: +200 m.
2. The pilot turns off the burner and allows the balloon to descend 60 m. Since the balloon is descending, we can represent this as a negative value: -60 m.
3. The pilot turns the burner on again and raises the balloon another 170 m. This upward movement can be represented as a positive value: +170 m.
So, the flight path can be represented as: +200 m, -60 m, +170 m.
b. To determine the total vertical distance traveled by the balloon, we use the absolute values of each stage of the flight path:
Absolute value of +200 m = 200 m
Absolute value of -60 m = 60 m
Absolute value of +170 m = 170 m
Adding these absolute values together, we get:
200 m + 60 m + 170 m = 430 m
Therefore, the total vertical distance traveled by the balloon is 430 m.
a. To represent each stage of the balloon's flight path using positive and negative values, we can assume that the ground level is the reference point at zero.
Initially, when the hot air balloon pilot raises the balloon 200 m from the ground, we can represent this as a positive value of +200 m.
When the pilot allows the balloon to descend 60 m, it means the balloon is going down. So, we can represent this as a negative value of -60 m.
Finally, when the pilot turns on the burner and raises the balloon another 170 m, we express this as a positive value of +170 m.
Therefore, the stages of the balloon's flight path can be represented as follows:
- Initial ascent: +200 m
- Descent: -60 m
- Final ascent: +170 m
b. To determine the total vertical distance traveled by the balloon, we need to consider the absolute value of each stage of the flight path and then sum them up.
The absolute value of a number is its magnitude without considering its sign. So, in this case, we take the positive value of each stage.
Absolute value of initial ascent: |200 m| = +200 m
Absolute value of descent: |-60 m| = +60 m
Absolute value of final ascent: |170 m| = +170 m
To find the total vertical distance traveled by the balloon, we simply sum up these absolute values.
Total vertical distance = +200 m + (+60 m) + (+170 m) = +430 m
Therefore, the total vertical distance traveled by the balloon is 430 meters.
height = 200 - 60 + 170 = 370 - 60 = 310
distance moved = |200| + |-60| + |170| = 200+60+170 = 430