While standing on top of a 256 m tall building, you see Iron Man flying straight down toward the ground at a speed of 32.0 m/s. Just as he passes you, you drop a can of Dr Pepper off the roof. How fast is the can going when it passes Iron Man?

when the can passes,

256 - 4.9t^2 = 256 - 32.0t

use that value of t for

v = -9.8t

ok thank you i got the right answer, but i do not understand where you got -4.9t^2 from. could you please explain that, so it helps me in the future.

Thanks

To find the speed of the can when it passes Iron Man, we need to consider the relative motion between the can and Iron Man.

First, let's analyze the motion of Iron Man. Since he is flying straight down towards the ground, his velocity can be considered constant throughout the motion. The speed of Iron Man is given as 32.0 m/s.

Now, let's analyze the motion of the can of Dr Pepper. Initially, the can is at rest on the rooftop. As it falls, it accelerates due to gravity towards the ground.

We can calculate the time it takes for Iron Man to pass the can using their relative positions. As Iron Man passes you, he is at a height of 256 m. The can is dropped from the same height, so the distance the can has fallen when Iron Man passes is also 256 m.

We know that the distance fallen by an object under free fall in time t is given by s = (1/2)gt^2, where g is the acceleration due to gravity (approximately 9.8 m/s^2 in this case). Since the can and Iron Man fall for the same distance, we have:

(1/2)gt^2 = 256 m

Solving for t, we find:

t = sqrt((2 * 256 m) / g)

Now that we have the time it takes for Iron Man to pass the can, let's calculate the speed of the can when it passes Iron Man.

The initial velocity of the can is 0 m/s, as it is dropped from rest. The acceleration due to gravity is -9.8 m/s^2 because it acts in the opposite direction of motion. We need to use the equation:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Substituting the values, we have:

v = 0 + (-9.8 m/s^2) * t

v = -9.8 m/s^2 * t

Now we can substitute the calculated value of t to find the speed of the can when it passes Iron Man:

v = -9.8 m/s^2 * (sqrt((2 * 256 m) / g))