a. The height for both the snowboarder and kangaroo is 0.5 feet.
b. The new height is 1 feet.
c. The relationship between hang time and height is linear in this case.
a. Given: t = 0.5 represents hang time.
To find the height (h), we can rearrange the equation:
t = 0.5 ⟹ h = 0.5
Therefore, the height for both the snowboarder and kangaroo is 0.5 feet.
b. Double the hang time (t);
t = 2 x 0.5
= 1
The new height (h) us h = 1
Therefore, doubling the hang time results in a height of 1 foot.
c. The relationship between hang time and height is linear in this case.
The formula t = 0.5 implies that for every unit increase in hang time, there is a corresponding increase of 0.5 units in height.
This linear relationship is consistent for both the snowboarder and kangaroo.
d. Other Relevant Considerations:
1. Gravity: The given function assumes constant gravity. In reality, variations in gravity could affect the hang time and height.
2. Jump Technique: Different jump techniques or styles can influence hang time and height.
3. Air Resistance: This model does not consider air resistance, which can have an impact on the actual jump.