A startled armadillo leaps upward rising .536 m in the first .197 s. What is its initial speed as it leaves the ground? What is its speed at the height of .536m? How much higher does it go?
To find the initial speed of the armadillo as it leaves the ground, we can use the kinematic equation:
vf = vi + at
Where:
vf is the final velocity (0 m/s, as the armadillo momentarily stops at its highest point)
vi is the initial velocity (what we're trying to find)
a is the acceleration (in this case, it would be due to gravity, which is approximately -9.8 m/s^2)
t is the time taken (0.197 s)
Rearranging the equation to solve for vi:
vi = vf - at
Since the final velocity (vf) at the highest point is 0 m/s, we can calculate the initial velocity:
vi = 0 - (-9.8 * 0.197)
vi = 1.9326 m/s
Therefore, the initial speed of the armadillo as it leaves the ground is approximately 1.9326 m/s.
To find the speed of the armadillo at a height of 0.536 m, we can use the kinematic equation again. However, we need to determine the time taken to reach that height.
Using the equation:
h = vi * t + (1/2) * a * t^2
Where:
h is the height (0.536 m)
vi is the initial velocity that we found earlier (1.9326 m/s)
a is the acceleration due to gravity (-9.8 m/s^2)
t is the time taken (what we're trying to find)
Rearranging the equation to solve for t:
0.536 = 1.9326 * t + (1/2) * (-9.8) * t^2
This equation is a quadratic equation that can be solved to find the value of t. Once t is determined, we can use it to find the speed at the height of 0.536 m using the equation:
vf = vi + at
Where:
vf is the final velocity (what we're trying to find)
vi is the initial velocity (1.9326 m/s)
a is the acceleration (-9.8 m/s^2)
t is the time taken (calculated from the quadratic equation)
Finally, to find how much higher the armadillo goes from its starting point, we can subtract the initial height (0 m) from the final height (0.536 m).
Note: The actual calculation of the time, final velocity, and the height difference will require solving the quadratic equation and performing the necessary calculations using the given values.