An arrow is shot straight up in the air with speed of 20m/s. How long is t in the air? How high will the arrow rise?

To determine the time the arrow is in the air, we can use the equation of motion for vertical motion:

h = ut + 0.5gt^2

Where:
h = height (unknown)
u = initial velocity (20 m/s)
g = acceleration due to gravity (-9.8 m/s^2, assuming we are on Earth)
t = time (unknown)

To find the time it takes for the arrow to reach its maximum height, we can use the fact that the vertical velocity (v) at the maximum height is 0.

v = u + gt
0 = u - gt

Rearranging this equation to solve for t:

t = u/g

Plugging in the values:
t = 20 m/s / 9.8 m/s^2
t ≈ 2.04 s

So, the arrow will remain in the air for approximately 2.04 seconds.

Now, to determine how high the arrow will rise, we can use the same equation of motion:

h = ut + 0.5gt^2

Plugging in the values:
h = (20 m/s)(2.04 s) + 0.5(9.8 m/s^2)(2.04 s)^2
h ≈ 20.4 m

Therefore, the arrow will rise to a height of approximately 20.4 meters.