Jane, looking for Tarzan, is running at top speed (4.3 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward?
V=4.3m/s
h=?
V=sqrt(2gh)
4.3^2=2gh (note:squaring both sides will cancel the square root on the right side)
18.49=2(9.8)(h)
18.49=19.6(h)
18.49/19.6=h
h=0.943367
To find how high Jane can swing upward, we need to consider the conservation of mechanical energy. When Jane grabs the vine, she only has kinetic energy from her running speed, which will convert into potential energy as she swings upward.
The equation we will use is:
Initial kinetic energy = Final potential energy
The initial kinetic energy can be calculated using the formula:
Kinetic energy = (1/2) * mass * velocity^2
However, since the problem does not provide information about Jane's mass, we can assume it's not relevant for finding the height she can swing.
Let's plug in the given values:
Jane's velocity, v = 4.3 m/s
Calculating the initial kinetic energy:
Initial kinetic energy = (1/2) * v^2
Initial kinetic energy = (1/2) * (4.3 m/s)^2
Initial kinetic energy = 9.315 J (rounded to three decimal places)
Now, let's find the corresponding potential energy when she reaches the highest point of the swing.
Potential energy = mass * gravity * height
Since Jane's mass is not given, we'll once again assume it's not relevant for finding the height she can swing. The value we need here is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Now we can rearrange the equation to solve for height:
Height = Potential energy / (mass * gravity)
Height = (Initial kinetic energy) / (mass * gravity)
As we've mentioned before, we can simplify the equation by assuming mass is not relevant for our calculations.
So, the height Jane can swing upward is equivalent to the potential energy she had when she grabbed the vine.
Height = Initial kinetic energy / gravity
Height = 9.315 J / 9.8 m/s^2
Height ≈ 0.949 meters
Jane can swing upward to a height of approximately 0.949 meters.