Final answer:
Using the kinematic equation that relates velocity, acceleration, and displacement, we find that the kangaroo reaches a height of 8.2 meters when its upward velocity slows to 8.0 m/s from an initial velocity of 15 m/s.
Step-by-step explanation:
To find out how high the kangaroo is when its velocity slows down to 8.0 m/s from an initial velocity of 15 m/s, we can use the following kinematic equation that relates velocity, acceleration, and displacement:
v^2 = u^2 + 2as
Where:
v is the final velocity (8.0 m/s),
u is the initial velocity (15 m/s),
a is the acceleration (in this case, the acceleration due to gravity, which is -9.8 m/s²), and
s is the displacement (the height we want to find).
Rearranging the equation to solve for s, we get:
s = (v^2 - u^2) / (2a)
Plugging in the values, we find:
s = ((8.0 m/s)² - (15 m/s)²) / (2 * -9.8 m/s²) = (64 - 225) / (-19.6) = 161 / 19.6 = 8.2 meters
The correct answer to how high the kangaroo is when it's traveling at 8.0 m/s is C. 8.2 meters.