While standing on top of a 323 m tall building, you see Iron Man flying straight down toward the ground at a speed of 35.0 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?
time to intercept:
323-35.0t = 323-4.9t^2
t = 7.14
http://www.wolframalpha.com/input/?i=323-35.0t+%3D+323-4.9t^2
Now, knowing that the can has speed
v = -9.8t
figure it out.
i need more help
what, you can't plug in t=7.14 into
-9.8t?
i did its giving me the wrong answer
well, if -69.972 is not right, then there may be an error in the answer key.
Did you try 69.972, since it just asks for speed, not velocity?
I can't see where I did anything wrong. Maybe someone else can spot a mistake.
To determine the speed of the can when it passes Iron Man, we need to consider the conservation of energy. Assuming no external forces, the total mechanical energy of the can-Iron Man system remains constant throughout their motion.
At the top of the building, the can has gravitational potential energy since it is at a height of 323 m. As it falls, this potential energy is converted into kinetic energy.
The equation for gravitational potential energy is:
PE = mgh
Where:
PE - Potential energy
m - Mass of the object (can)
g - Acceleration due to gravity (approximately 9.8 m/s²)
h - Height of the object (323 m)
Next, we calculate the kinetic energy of the can when it passes Iron Man. The equation for kinetic energy is:
KE = (1/2)mv²
Where:
KE - Kinetic energy
m - Mass of the object (can)
v - Velocity of the object
Since the can was initially at rest, its initial kinetic energy was zero. Therefore, all of the potential energy is converted into kinetic energy:
PE = KE
mgh = (1/2)mv²
In this equation, the mass of the can cancels out, leaving us with:
gh = (1/2)v²
Simplifying, we have:
v² = 2gh
Plugging in the values:
g = 9.8 m/s²
h = 323 m
v² = 2 * 9.8 m/s² * 323 m
Calculating this expression, we find that v² = 6320.8 m²/s².
To determine the velocity (v) of the can when it passes Iron Man, we take the square root of v²:
v = √6320.8 m²/s² ≈ 79.5 m/s
Therefore, the can of Dr Pepper is traveling approximately 79.5 m/s when it passes Iron Man.