Calculating Kangaroo's Minimum Vertical Speed
What is the minimum vertical speed of a kangaroo when it leaves the ground?
Given data:
- Maximum height (h) = 1.8 m
- Final velocity (v) = 0 m/s (at maximum height)
- Acceleration due to gravity (g) = 9.8 m/s²
Calculation of Kangaroo's Minimum Vertical Speed
To determine the minimum vertical speed of the kangaroo when it leaves the ground, we can use the formula:
v² = u² - 2gh
Given that v = 0 m/s, h = 1.8 m, and g = 9.8 m/s², we can solve for u:
0 = u² - 2(9.8)(1.8)
0 = u² - 35.28
u² = 35.28
u = √35.28
u ≈ 5.94 m/s
Therefore, the minimum vertical speed of the kangaroo when it leaves the ground is approximately 5.94 m/s.
When a kangaroo jumps over an object 1.8 m high, its minimum vertical speed as it leaves the ground is crucial for a successful leap. By applying the principle of motion under gravity, we can calculate this speed using the given data. The formula v² = u² - 2gh relates the final velocity (v), initial velocity (u), height (h), and acceleration due to gravity (g).
Substituting the values into the formula and solving for u, we find that the kangaroo's minimum vertical speed is approximately 5.94 m/s. This speed enables the kangaroo to achieve the necessary height and distance to clear the obstacle successfully.
Understanding the physics behind the kangaroo's jump not only provides insight into its remarkable abilities but also highlights the importance of velocity and acceleration in vertical motion. By mastering these concepts, we can appreciate the agility and strength of these extraordinary animals.