While standing on top of a 220. m tall building, you see Iron Man flying straight down toward the ground at a speed of 30.0 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?
i dont understand
To determine the velocity of the can of Dr Pepper when it passes Iron Man, we need to first consider the motion of Iron Man as he flies straight down toward the ground.
Since Iron Man is flying straight down, his initial velocity is 30.0 m/s downward. The can of Dr Pepper, on the other hand, is initially at rest, so its initial velocity is 0.
Next, we need to calculate the time it takes for Iron Man to pass the building. We can use the equation for time:
time = distance / velocity
The distance in this case is the height of the building, which is given as 220.0 m. The velocity is given as 30.0 m/s. Plugging these values into the equation, we get:
time = 220.0 m / 30.0 m/s = 7.33 s
So it takes Iron Man 7.33 seconds to pass the building.
Now, to determine the velocity of the can when it passes Iron Man, we need to consider the time it takes for the can to fall from the roof to the point where Iron Man passes the building. This time can be calculated using the equation of motion for free-falling objects:
distance = (1/2) * acceleration * time^2
Since the can falls freely under gravity, the acceleration is approximately 9.8 m/s^2. The distance is the height of the building, which is 220.0 m.
220.0 m = (1/2) * 9.8 m/s^2 * t^2
Simplifying the equation, we have:
t^2 = (220.0 m * 2) / 9.8 m/s^2
t^2 = 44.9
Taking the square root of both sides, we find:
t = 6.70 s
So it takes approximately 6.70 seconds for the can to fall from the roof to the point where Iron Man passes the building.
Now, we can calculate the final velocity of the can by using the formula for velocity:
final velocity = initial velocity + acceleration * time
Since the initial velocity of the can is 0, and the acceleration is due to gravity (-9.8 m/s^2), we can plug in the values:
final velocity = 0 + (-9.8 m/s^2) * 6.70 s
final velocity = -65.66 m/s
The negative sign indicates that the can is moving downward. Therefore, the can of Dr Pepper is going at a speed of 65.66 m/s when it passes Iron Man.
I hate these busy work problems.
the man at 30 and the falling can will have gone the same distance, solve for the time that happens
30*t=gt^2
then, the velocity at that point in time: vf=g*t