A startled armadillo leaps upward, rising .544 m in eh first .200s

a) What is its initial speed as it leaves the ground?

b)What is its speed at the height of .544m?

c) How much higher does it go?

Solve the first part
d= vo*t - 1/2 9.8 t^2
you know d, and t.
solve for vo.
For the second part, vf=vo- 9.8 t

For the final height, the vf is zero, so
Vf=vot- 9.8 t solve for t then put it in the displacement equation to get max height.

1.74

3.7
0.698

wow, anonymous you're so helpful. not. work and step-by-step would help.

a) To calculate the initial speed (vo) as the armadillo leaves the ground, we can use the equation of motion:

d = vo * t - 1/2 * 9.8 * t^2

Given that the displacement (d) is 0.544 m and the time (t) is 0.200 s, we can rearrange the equation to solve for vo:
vo = (d + 1/2 * 9.8 * t^2) / t

Substituting the values:
vo = (0.544 + 1/2 * 9.8 * 0.200^2) / 0.200

Now we can solve for vo:
vo = (0.544 + 0.196) / 0.200
vo = 0.740 m/s

Therefore, the initial speed of the armadillo as it leaves the ground is 0.740 m/s.

b) To calculate the speed at the height of 0.544 m, we can use the equation:
vf = vo - 9.8 * t

Since the armadillo is at its maximum height, vf = 0. So we have:
0 = vo - 9.8 * t

From part a, we know that vo = 0.740 m/s. Rearranging the equation, we can solve for t:
t = vo / 9.8

Substituting the value:
t = 0.740 / 9.8
t = 0.0755 s

Now we can calculate the speed at the height of 0.544 m:
vf = vo - 9.8 * t
vf = 0.740 - 9.8 * 0.0755

Solving for vf:
vf ≈ 0.0066 m/s

Therefore, the speed of the armadillo at the height of 0.544 m is approximately 0.0066 m/s.

c) To calculate how much higher the armadillo goes, we need to find the maximum height it reaches. At this point, the final velocity (vf) is zero. Using the equation of motion:

vf = vo * t - 1/2 * 9.8 * t^2

Since vf is zero, we have:
0 = vo * t - 1/2 * 9.8 * t^2

Simplifying the equation:
9.8 * t^2 = vo * t

Solving for t:
t = vo / 9.8

Substituting the value of vo (0.740 m/s) we obtained from part a:
t = 0.740 / 9.8
t = 0.0755 s

Now we can calculate the maximum height (h) that the armadillo reaches using the displacement equation:
h = vo * t - 1/2 * 9.8 * t^2

Substituting the values:
h = 0.740 * 0.0755 - 1/2 * 9.8 * 0.0755^2

Solving for h:
h ≈ 0.0277 m

Therefore, the armadillo goes approximately 0.0277 m higher from its initial position.