Felix Baumgartner, an Austrian skydiver, jumped from a balloon at an altitude of 38,963.3 meters, and fell into history. He was in free fall for 4 minutes 19 seconds, and on the way down reached the speed of 1,357.64 km/h
What if there had been no air? How long would it have taken him to reach 1357.64 km/hr? How long did it actually take him to reach this speed?
In the absence of air, how long would it have taken him to reach the ground, and what speed would he have reached by the time he got there?
For Felix's fall, is his downward acceleration the same all the way down?
a: no resistance,
vf=g*t
change speed to m/s
vf=1357.64km/hr*1hr/3600sec*1000m/1km
vf=377.1 m/s
t= 377.1/9.8=38 seconds with no air resistance
<how long did it actually take to reach the speed?>
avg speed= distance/time=38.96km/259sec=150m/s
so you can figure the average speed during the accelerating time, and a terminal speed for the rest.
ta= time accelerating
tt= time terminal
ta+tt=259sec
150*ta+377(259-ta)=38.96km
solve for ta.
<free fall:
d=1/2 g t^2
t=sqrt 2*38.9k/9.8=sqrt(7930)=89 sec
final speed:
vf=g*t=9.8*89 m/s
To determine how long it would have taken Felix Baumgartner to reach 1,357.64 km/h in the absence of air, we can use the basic principles of motion in freefall.
The formula to calculate the time it takes to reach a certain speed in freefall is:
time = (final speed - initial speed) / acceleration
In this case, the initial speed is 0 m/s (as he starts from rest) and the final speed is 1,357.64 km/h. We need to convert the final speed from km/h to m/s because the acceleration will be in units of m/s^2.
To convert km/h to m/s, we divide the speed by 3.6:
1,357.64 km/h = 1,357.64 * (1000 m/1 km) / (3600 s/1 h) = 376.57 m/s
Now we can calculate the time it would have taken for Felix to reach this speed in the absence of air:
time = (376.57 m/s - 0 m/s) / acceleration
In the absence of air, the only force acting on Felix would be the force of gravity, so his acceleration is equal to the acceleration due to gravity, denoted as "g".
The value of acceleration due to gravity on Earth is approximately 9.8 m/s^2, so we can substitute this value into the equation:
time = (376.57 m/s - 0 m/s) / 9.8 m/s^2
Calculating this, we find that it would have taken Felix approximately 38.44 seconds to reach a speed of 1,357.64 km/h in the absence of air.
Now, let's calculate how long it actually took Felix to reach this speed using the given information.
We are given that Felix was in freefall for 4 minutes and 19 seconds, which we can convert to seconds:
4 minutes 19 seconds = (4 * 60 seconds) + 19 seconds = 259 seconds
Since the given time includes the time he was already in freefall, we can subtract the time it took him to reach the desired speed from the given total time to find the additional time it took him beyond that point:
additional time = given time - time to reach desired speed
additional time = 259 seconds - 38.44 seconds
Therefore, it took Felix an additional 220.56 seconds (or approximately 3 minutes 40.56 seconds) to reach a speed of 1,357.64 km/h.
In the absence of air, we can also calculate how long it would have taken Felix to reach the ground and the speed he would have reached.
To calculate the time it takes to reach the ground, we need to use a different formula for distance in freefall:
distance = (1/2) * acceleration * time^2
In this case, the distance is equal to the altitude from which Felix jumped, which is 38,963.3 meters. We can solve for time:
38,963.3 = (1/2) * 9.8 * time^2
Simplifying the equation, we find:
time^2 = (2 * 38,963.3) / 9.8
time^2 = 7,949.24
time ≈ √7,949.24 ≈ 89.14 seconds
Therefore, in the absence of air, it would have taken Felix approximately 89.14 seconds to reach the ground.
To calculate the speed at which he would have reached the ground, we can use the formula:
final speed = initial speed + acceleration * time
Since he starts from rest, the initial speed is 0 m/s. The acceleration is still equal to gravity (9.8 m/s^2), and the time is 89.14 seconds.
Thus, the speed at which Felix would have reached the ground in the absence of air is approximately:
final speed = 0 + 9.8 * 89.14 ≈ 871.97 m/s.
As for Felix's downward acceleration during freefall, it is not constant all the way down. Initially, his acceleration is around 9.8 m/s^2, but as he gains speed and the force of air resistance becomes significant, his acceleration decreases. Eventually, it reaches a point where his acceleration becomes zero, and he falls with a constant terminal velocity.