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=4.3
g=9.8
GPE=KE
mgh=(1/2)mv^2
mass cancels out so;
gh=(1/2)v^2
plug in your values and you should get the right answer
To determine how high Jane can swing upward, we can use the conservation of mechanical energy principle.
The initial energy when she grabs the vine hanging vertically from the tall tree is purely kinetic energy, given by:
KE_initial = (1/2) * m * v_initial^2
where m is Jane's mass and v_initial is her initial speed.
Next, we need to consider the maximum height Jane can reach while swinging upward. At the highest point, all the initial kinetic energy is converted into potential energy. Therefore, the equation becomes:
PE_max = m * g * h_max
where g is the acceleration due to gravity and h_max is the maximum height she can reach.
Since energy is conserved, we can equate the initial kinetic energy and the maximum potential energy:
KE_initial = PE_max
(1/2) * m * v_initial^2 = m * g * h_max
Simplifying the equation and solving for h_max, we get:
h_max = (v_initial^2) / (2 * g)
Substituting the given values:
v_initial = 4.3 m/s
g = 9.8 m/s^2 (approximate value)
h_max = (4.3^2) / (2 * 9.8)
Calculating this, we find:
h_max ≈ 0.94 meters
Therefore, Jane can swing upward to a maximum height of approximately 0.94 meters.
To determine how high Jane can swing upward, we need to consider the conservation of mechanical energy. When Jane grabs the vine, she converts her kinetic energy into potential energy as she swings upward.
The formula for gravitational potential energy is:
PE = mgh
Where:
PE is the potential energy (Joules)
m is the mass of the object (kg)
g is the acceleration due to gravity (9.8 m/s²)
h is the height above a reference point (m)
In this case, we can assume that Jane's mass is irrelevant because the question is interested in the maximum height she can swing.
Given that Jane is running at a speed of 4.3 m/s before grabbing the vine, we can determine her initial kinetic energy (KE) using the formula:
KE = (1/2)mv²
Where:
KE is the kinetic energy (Joules)
m is the mass of the object (kg)
v is the velocity/speed of the object (m/s)
Since Jane's mass is not given, we can leave it as a variable "m" since it cancels out in the final equation.
Using the initial kinetic energy, we can equate it to the potential energy at the highest point of Jane's swing:
(1/2)mv² = mgh
Since the mass "m" cancels out, we can solve for h:
(1/2)v² = gh
Rearranging the equation:
h = (1/2)(v²/g)
Now we can substitute the values:
h = (1/2)(4.3²/9.8)
Calculating this equation, we find:
h ≈ 0.9404 meters
Therefore, Jane can swing approximately 0.9404 meters or about 94 centimeters upward when she grabs the vine.