e. Felix Baumgartner is a daredevil famous for breaking the sound barrier during a freefall on October 14, 2012. Aided by a weather balloon, he climbed to a height of 128,100 feet. More than 24 miles in the air, he was so high up that he could see Earth’s curvature. He then jumped out of the capsule that carried him. On the way down, he traveled at an average of 335.92 miles per hour, at one point even going as fast as 720 miles per hour, breaking the record for the highest skydive ever attempted and breaking the sound barrier in the process. Using the formula you derived in part b, how long did it take Baumgartner to reach the ground, in minutes? Be careful about unit conversions, and show your work.
what a lot of noise.
Distance traveled: 128100 ft = 24.26 mi
Average speed: 335.92 mi/hr
so, time falling is 24.26mi / 335.92mi/hr = 0.0722hr = 4.3 minutes
Well, let's calculate the time it took for Baumgartner to reach the ground.
The formula we derived in part b is:
time = distance / speed
So, the distance he traveled was 128,100 feet (or approximately 24.26 miles).
Converting this distance to meters, we have:
distance = 24.26 miles * 1609.34 meters/mile ≈ 39,014.84 meters
Now, let's convert his average speed of 335.92 miles per hour to meters per second:
speed = 335.92 miles/hour * 1609.34 meters/mile / 3600 seconds/hour ≈ 150.69 meters/second
Using the formula:
time = distance / speed
time = 39,014.84 meters / 150.69 meters/second ≈ 258.89 seconds
To convert this time to minutes, we divide by 60:
time = 258.89 seconds / 60 ≈ 4.31 minutes
So, it took Baumgartner approximately 4.31 minutes to reach the ground during his historic skydive.
To calculate the time it took Felix Baumgartner to reach the ground, we can use the formula derived in part b:
t = (2 * v) / g
Where:
t = time
v = average velocity = 335.92 miles per hour
g = acceleration due to gravity = 32.174 ft/s^2
First, let's convert the average velocity from miles per hour to feet per second:
v = 335.92 miles per hour * 5280 feet per mile / 3600 seconds per hour = 489.47 feet per second
Now we can substitute the values into the formula and solve for t:
t = (2 * 489.47 feet per second) / 32.174 feet per second^2
t = 30.45 seconds
Since the question asks for the time in minutes, let's convert seconds to minutes:
t = 30.45 seconds * 1 minute / 60 seconds
t = 0.5075 minutes
Therefore, it took Felix Baumgartner approximately 0.5075 minutes (or about 30.45 seconds) to reach the ground.
To find how long it took Felix Baumgartner to reach the ground, we need to use the equation of motion which we derived in part b:
t = sqrt((2*d) / g)
Where:
t = time taken to reach the ground
d = distance traveled during the freefall
g = acceleration due to gravity
In this case, the distance traveled during the freefall can be calculated as:
d = 128,100 feet (height climbed by Felix Baumgartner) - 24 miles (distance in the air, which is equal to 24 * 5280 feet)
First, let's convert the distance to feet:
24 miles * 5280 feet/mile = 126,720 feet
Now, we can calculate the distance traveled during the freefall:
d = 128,100 feet - 126,720 feet = 1,380 feet
Next, we need to convert this distance to meters, as the acceleration due to gravity is usually given in m/s^2. Since 1 foot is approximately 0.3048 meters, we have:
1,380 feet * 0.3048 meters/foot = 420.384 meters
Now, we can substitute the value of distance (d) and acceleration due to gravity (g) into the equation to calculate the time (t):
t = sqrt((2 * 420.384) / 9.8)
= sqrt(840.768 / 9.8)
= sqrt(85.8747)
So, it took Baumgartner approximately sqrt(85.8747) seconds to reach the ground. To convert this to minutes, we need to divide by 60:
t (in minutes) = sqrt(85.8747) / 60
Now, we can calculate this value using a calculator, which gives:
t (in minutes) ≈ 0.4472 / 60
≈ 0.0075 minutes
Therefore, it took Felix Baumgartner approximately 0.0075 minutes (or approximately 0.45 seconds) to reach the ground during his record-breaking skydive.