A sky diver of mass 80.0 ks jumps from a slow-moving aircraft and reaches a terminal speed of 50.0 m/s. a) What is the acceleration of the sky diver when her speed is 30.0 m/s? What is the drag force on the diver when her speed is b) 50.0 m/s? c) 30.0 m/s?
If you assume drag force is proportional to speed, then
dragforce= k*speed
and at terminal speed, dragforce=weight.
80kg*g=k*40m/s
so you can calculate k.
Then, calculate the drag force at 30.
wait, where did you get the 40 m/s?
and i still don't understand how to find the acceleration.
and if i calculate k that way..then wouldn't the value of k change when her speed changes?
40 was a typo, should have been 50.
vfinal^2 -vinitial^2= 2*acceleration*distance
but distance= average velocity *time
= (Vfinal + Vinitial )/2
solve for acceleration.
k is a constant, it wont change with speed if you assume linear proportionality.
Given m = 80.0 kg, vT = 50.0 m/s, we write
mg = DρAvT
2
2
which gives
DρA
2
= mg
vT
2 = 0.314 kg m
(a) At v = 30.0 m/s,
a = g − DρAv2 2
m
= 9.80 m/s2 −
(0.314 kg/m)(30.0 m/s)2
80.0 kg
= 6.27 m/s2 downward
(b) At v = 50.0 m/s, terminal velocity has been reached.
Fy Σ = 0 = mg − R
⇒R = mg = (80.0 kg)(9.80 m s2 ) = 784 N directed up
(c) At v = 30.0 m/s,
DρAv2
2
= (0.314 kg/m)(30.0 m/s)2 = 283 N upward
To find the acceleration of the skydiver when her speed is 30 m/s, we can use the equation:
vf^2 - vi^2 = 2 * acceleration * distance
where vf is the final velocity (30 m/s), vi is the initial velocity (0 m/s since she jumps from a slow-moving aircraft), and distance is the total distance traveled.
Since we don't know the distance traveled, we can use the average velocity * time formula to find it. The average velocity is the sum of the initial and final velocities divided by 2:
distance = (vf + vi) / 2
Substituting the values:
distance = (30 m/s + 0 m/s) / 2
distance = 15 m
Now we can calculate the acceleration:
30^2 - 0^2 = 2 * acceleration * 15
900 = 30 * acceleration
Divide both sides by 30:
acceleration = 900 / 30
acceleration = 30 m/s^2
Therefore, the acceleration of the skydiver when her speed is 30 m/s is 30 m/s^2.
Now let's move on to the drag force. Assuming drag force is proportional to speed, we can use the equation:
drag force = k * speed
where k is a constant. We are given that at terminal speed, the drag force is equal to the weight of the skydiver.
Therefore, at terminal speed (50 m/s), the drag force is equal to the weight:
drag force = weight
Let's calculate the weight first:
weight = mass * acceleration due to gravity
weight = 80 kg * 9.8 m/s^2
weight = 784 N
Now, let's find the value of the constant k. At terminal speed, the drag force is equal to the weight:
k * 50 m/s = 784 N
Solving for k:
k = 784 N / 50 m/s
k = 15.68 N s/m
Now, to calculate the drag force at 30 m/s, we can use the value of k:
drag force = k * speed
drag force = 15.68 N s/m * 30 m/s
drag force = 470.4 N
Therefore, the drag force on the skydiver when her speed is 30 m/s is 470.4 N.
For the drag force at 50 m/s, we can use the value of k again:
drag force = k * speed
drag force = 15.68 N s/m * 50 m/s
drag force = 784 N
Therefore, the drag force on the skydiver when her speed is 50 m/s is also 784 N.
To find the acceleration of the skydiver when her speed is 30.0 m/s, you can use the equation:
vfinal^2 - vinitial^2 = 2 * acceleration * distance
Since the skydiver is already at terminal speed, her final velocity (vfinal) is equal to her terminal speed, which is 50.0 m/s. The initial velocity (vinitial) is 30.0 m/s. The distance will depend on the time it takes for her to change her speed from 30.0 m/s to 50.0 m/s.
To find the distance, you can use the equation:
distance = average velocity * time
Since the average velocity is (vfinal + vinitial)/2 and we need to know the time it takes to change from 30.0 m/s to 50.0 m/s, we can rearrange the equation:
time = distance / average velocity
The value of the average velocity will be (30.0 m/s + 50.0 m/s)/2.
Once you have the time, you can substitute the values into the first equation to solve for acceleration.
Regarding the drag force, if you assume that the drag force is proportional to speed, then you can write it as:
drag force = k * speed
At terminal speed, the drag force is equal to the weight of the skydiver. So, you can set up an equation using the weight of the skydiver, which is equal to mass (80.0 kg) multiplied by the acceleration due to gravity (9.8 m/s^2):
weight = k * terminal speed
Solving for k will give you the constant of proportionality. Once you have k, you can calculate the drag force at any given speed. For example, to find the drag force at 30.0 m/s, you can substitute the value of speed into the equation drag force = k * speed.