When sky divers initially fall from an airplane their velocity v in miles per hour after free falling d feet can be approximated by v=60/11√d. (Because of air resistance, they will eventually reach terminal velocity.) How far do sky divers need to fall to attain a velocity of 55 miles per hour? (This value for d represents the minimum distance.)
A sky diver needs to fall about ? feet to attain a velocity of 55mph.
55 = 60/11 √d
10.08 = √d
101.67 = d
Can you explain how you got the answer above!
Well, well, well, it seems like these skydivers want to go fast! Let's do some calculations to figure out how far they need to fall to reach that velocity.
Now, we're given that the velocity v in miles per hour is given by the lovely formula v = 60/11√d. And we're looking for the minimum distance d needed for a velocity of 55 miles per hour.
So, let's plug in the velocity we want, v = 55, into the formula. We get 55 = 60/11√d.
Now, to make this mathematically simpler, let's square both sides of the equation. We get 55^2 = (60/11√d)^2.
Oh, dear numbers, don't you all love squaring things? [Please don't answer, numbers can't talk.]
That simplifies to 3025 = (3600/121)d.
And now, let's solve for d, the distance they need to fall. We multiply both sides by 121/3600, and voila! We get d ≈ 15.24 feet.
So, skydivers, if you want to reach a velocity of 55 miles per hour, you'll need to fall approximately 15.24 feet. Just don't forget to deploy that parachute at the right time! Safety first, my friends!
To find the distance (d) the sky divers need to fall in order to attain a velocity of 55 miles per hour, we can use the given equation:
v = 60/11√d
Given that v = 55 mph, we can substitute this value into the equation:
55 = 60/11√d
To solve for d, we can start by multiplying both sides of the equation by 11:
605 = 60√d
Next, divide both sides of the equation by 60:
605/60 = √d
Simplifying the left side:
10.08333333 = √d
To isolate d, we need to square both sides of the equation:
(10.08333333)^2 = (√d)^2
101.6756944 = d
Therefore, sky divers need to fall about 101.6756944 feet to attain a velocity of 55 mph.
To find the distance (d) the skydiver needs to fall to attain a velocity of 55 miles per hour, we can start by using the given formula:
v = 60/11√d
The formula gives the velocity (v) in miles per hour depending on the distance (d) in feet. We are given that the velocity should be 55 miles per hour, so we can substitute this value into the formula and solve for d.
55 = 60/11√d
Let's solve this equation step by step:
Step 1: Multiply both sides of the equation by 11 to eliminate the fraction:
55 * 11 = 60√d
605 = 60√d
Step 2: Divide both sides of the equation by 60 to isolate the square root:
605/60 = √d
10.08 = √d
Step 3: Square both sides of the equation to eliminate the square root:
(10.08)^2 = (√d)^2
101.6064 = d
Therefore, a skydiver needs to fall about 101.6064 feet to attain a velocity of 55 mph.