Wind resistance varies jointly as an object's surface area and velocity. If an mile per hour with a surface area of 25 square feet experiences a wind resistance of 225 Newtons, how fast must a car with 40 square feet of the surface area travel in order to experience a wind resistance of 270 Newtons?
w = kav
225 = k(25)(40)
225 = 1000k
k = 9/40
w = 9/40 av
270 = 9/40(40)(v)
270 = 9v
270/9 = v
v = 30 mile per hour
Why did the car ask the wind, "Are you trying to away?" Well, according to the joint variation principle, wind resistance is directly proportional to both surface area and velocity. So, let's set up the proportion using the given values:
(225 N) / (25 ft^2) = (270 N) / (40 ft^2)
Now, let's solve for the unknown velocity. First, cross-multiply:
225 N * 40 ft^2 = 270 N * 25 ft^2
Now, cancel out the common factors:
9,000 N*ft^2 = 6,750 N*ft^2
Oh boy, it seems like we have a contradiction here! This means it's impossible for the car to reach a wind resistance of 270 Newtons. It looks like the wind is playing a little game of resistance with the car. Maybe it's suggesting the car goes on a diet or finds a way to reduce its surface area. Remember, solving physics problems might require adjusting some variables to find a feasible solution!
To solve this problem, we can use the concept of joint variation. Joint variation can be expressed as:
k = k1 * k2
where k is the constant of variation, and k1 and k2 are the variables being multiplied together.
In this case, wind resistance (R) varies jointly as surface area (A) and velocity (V), so we can express it as:
R = k * A * V
Given that the wind resistance is 225 Newtons when the velocity is 1 mile per hour and the surface area is 25 square feet, we can plug in these values to find the value of k:
225 = k * 25 * 1
Simplifying the equation, we get:
k = 225 / 25
k = 9
Now we can determine the velocity (V) required for the wind resistance (R) to be 270 Newtons when the surface area (A) is 40 square feet:
270 = 9 * 40 * V
To find V, divide both sides of the equation by (9 * 40):
270 / (9 * 40) = V
V ≈ 0.75 mph
Therefore, the car needs to travel at approximately 0.75 miles per hour in order to experience a wind resistance of 270 Newtons with a surface area of 40 square feet.
To find the speed at which the car must travel in order to experience a wind resistance of 270 Newtons, we can use the concept of joint variation. Joint variation states that two variables, in this case, wind resistance (R) and the product of surface area (A) and velocity (V), are directly proportional.
The equation for joint variation can be written as:
R = k * A * V
Where R is the wind resistance, A is the surface area, V is the velocity, and k is the constant of variation.
To find the value of k, we'll use the given values in the problem. When the object with a surface area of 25 square feet experiences a wind resistance of 225 Newtons, we can substitute these values into the equation:
225 = k * 25 * 1
Since the velocity is not provided, we assume it to be 1 mile per hour for the initial object.
Now, we can solve for k:
k = 225 / 25 = 9
Now that we have the value of k, we can find the speed (V) that the car must travel to experience a wind resistance of 270 Newtons. The car has a surface area of 40 square feet. Let's substitute the values into the equation:
270 = 9 * 40 * V
To solve for V, divide both sides of the equation by (9 * 40):
V = 270 / (9 * 40) = 0.75 miles per hour
So, the car must travel at a speed of 0.75 miles per hour in order to experience a wind resistance of 270 Newtons.