1) While standing on top of a 360. m tall building, you see Iron Man flying straight down toward the ground at a speed of 34.0 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?
To find the speed of the can when it passes Iron Man, we need to apply the principles of relative motion. Let's break the problem down step by step:
1) First, let's find the time it takes for Iron Man to reach the can. We can use the formula for time: time = distance / speed.
The distance is the height of the building, which is 360.0 m, and the speed is Iron Man's speed, which is 34.0 m/s.
So, the time taken by Iron Man to reach the can is: time = 360.0 m / 34.0 m/s = 10.588 seconds (rounded to three decimal places).
2) Now, we need to find the can's speed when it passes Iron Man. The can is dropped from rest, so its initial speed is 0 m/s.
Since only gravity acts on the can, it will accelerate downward at a constant rate due to gravity (9.8 m/s^2) throughout its fall.
Using the equation of motion: final velocity = initial velocity + acceleration * time, we can find the final velocity of the can.
Given that the initial velocity (u) is 0 m/s, the acceleration (a) is -9.8 m/s^2 (negative because it is pointing downward), and the time (t) is 10.588 seconds, we can calculate the final velocity (v).
v = 0 m/s + (-9.8 m/s^2) * 10.588 s = -103.384 m/s (rounded to three decimal places).
3) However, speed is always positive, so we take the absolute value of the result. Thus, the speed of the can when it passes Iron Man is approximately 103.384 m/s.
Therefore, the can of Dr Pepper will be traveling at a speed of around 103.384 m/s when it passes Iron Man.