A kangaroo jumps to a vertical height of 242 cm. How long (in seconds) was the kangaroo in the air?

s = 4.9t^2

.242/4.9 = t^2
t = .22 sec
That's how long it took to jump up. After landing back on earth, total time in the air was .44 sec

To determine the time the kangaroo was in the air, we can use the principles of kinematics. Specifically, we can use the equation for vertical motion:

Δy = v₀t + (1/2)gt²

where:
Δy = vertical displacement (242 cm in this case)
v₀ = initial vertical velocity (0 cm/s since the kangaroo jumps up from rest)
t = time in seconds
g = acceleration due to gravity (approximately 980 cm/s²)

Rearranging the equation, we get:

Δy = (1/2)gt²

Substituting the known values, we have:

242 cm = (1/2)(980 cm/s²)t²

Now, let's solve for t.

First, multiply both sides of the equation by 2 to get rid of the fraction:

484 cm = 980 cm/s² * t²

Next, divide both sides of the equation by 980 cm/s²:

t² = 484 cm / 980 cm/s²

Simplify the right side of the equation:

t² = 0.4949 s²

Finally, take the square root of both sides of the equation to solve for t:

t = √0.4949 s²

t ≈ 0.704 s

Therefore, the kangaroo was in the air for approximately 0.704 seconds.