Kangaroos' Impressive Jumping Ability
How can we calculate a kangaroo's minimum vertical speed when it leaves the ground based on its jumping abilities?
From the data provided, what are the key factors we need to consider in determining the kangaroo's initial velocity?
Calculation of Kangaroo's Minimum Vertical Speed
To calculate the kangaroo's minimum vertical speed, we can use the formula:
v² = u² - 2gh
where,
v = final velocity (0 m/s at maximum height)
u = initial velocity (unknown)
g = acceleration due to gravity (9.8 m/s²)
h = maximum height (1.8 m)
When the kangaroo is at its maximum height of 1.8m, its final velocity is 0 m/s. By substituting these values into the formula and solving for the initial velocity, we can determine the kangaroo's minimum vertical speed when it leaves the ground.
Substitute v = 0, h = 1.8m, and g = 9.8 m/s² into the formula:
0² = u² - 2(9.8)(1.8)
0 = u² - 35.28
Now, solve for u:
u² = 35.28
u = √35.28 = 5.94 m/s
Therefore, the kangaroo's minimum vertical speed when it leaves the ground is 5.94 m/s.