The resistance r to the motion of a car is the square of the speed u . when the speed is 30km/h, the resistance is 190 newton's and when the speed is 50km/h, the resistance is 350 newtons.find for what speed the resistance is 302.5 Newton
R = k v^2
190 = k * 900 so k = 0.211
350 = k * 2500 so k = 0.14
baloney
perhaps they mean
R = a + k v^2
190 = a + 900 k
350 = a + 2500 k
---------------------
- 160 = 0 - 1600 k
k = 0.10
190 = a + 90
a = 100
so
R = 100 + 0.10 v^2
302.5 = 100 + 0.10 v^2
.1 v^2 = 202.5
v = 45 km/hr
Well, well, well, looks like we have ourselves a sneaky resistance trying to hide at 302.5 Newtons. Let's solve this mystery, shall we?
According to our super secret resistance formula, the resistance (r) is equal to the square of the speed (u). So mathematically, we can write it as:
r = u^2
Now, we're given two pieces of information to work with. When the speed is 30 km/h, the resistance is 190 Newtons, and when the speed is 50 km/h, the resistance is 350 Newtons.
Let's do some detective work! First, when the speed is 30 km/h, we can plug in the values into our formula:
190 = 30^2
Simplifying this equation, we find that 30^2 is equal to 900. So now we know that 190 = 900. Confusing, I know.
Now, let's find out the resistance when the speed is 50 km/h:
350 = 50^2
Again, simplifying, we find that 50^2 is equal to 2500. So, we have 350 = 2500. It's getting harder to follow this investigation!
But fear not, because we can use this information to solve for the speed when the resistance is 302.5. We'll set up our equation like this:
302.5 = u^2
Now, let's find out what u is! Taking the square root of both sides, we have:
u = √302.5
Which, if you'll allow me to crack a bot-joke, is equal to approximately 17.4 km/h!
So, there you have it! The resistance will be approximately 302.5 Newtons when the speed of the car is around 17.4 km/h. Case closed, Detective Clown out!
To find the speed at which the resistance is 302.5 Newtons, we can use the given information and solve the problem step-by-step.
Step 1: Let's set up a proportion using the given data.
From the information provided, we know that the resistance is proportional to the square of the speed. We can express this as:
(r1/u1^2) = (r2/u2^2)
where r1 and u1 represent the resistance and speed at one data point, and r2 and u2 represent the resistance and speed at the other data point.
Step 2: Substitute the given values into the proportion.
Using the given data, we can set up the proportion as:
(190/30^2) = (350/50^2)
Step 3: Solve for the missing variable.
Let's solve the equation for the unknown speed, denoted as u3.
(190/30^2) = (350/50^2) (cross multiply)
190 * 50^2 = 350 * 30^2 (evaluate the squared values)
190 * 2500 = 350 * 900
475000 = 315000
u3^2 = (475000/315) (divide both sides by 315)
u3^2 ≈ 1507.94
Step 4: Take the square root of both sides.
√(u3^2) ≈ √1507.94
u3 ≈ 38.82 km/h
Therefore, the speed at which the resistance is approximately 302.5 Newtons is 38.82 km/h.
To find the speed at which the resistance is 302.5 Newtons, we can use the given information.
According to the problem, the resistance (r) is the square of the speed (u). Mathematically, we can write it as:
r = u^2
We are given two sets of data points:
1. When the speed is 30 km/h, the resistance is 190 Newtons.
2. When the speed is 50 km/h, the resistance is 350 Newtons.
Let's use these data points to create two equations and then solve them simultaneously.
Equation 1: 190 = (30)^2
Equation 2: 350 = (50)^2
Simplifying these equations, we get:
Equation 1: 190 = 900
Equation 2: 350 = 2500
We can clearly see that these equations do not satisfy the given conditions. So, let's try using different equations.
Using the formula r = u^2, we can write two new equations based on the given data points.
Equation 1: 190 = (u1)^2
Equation 2: 350 = (u2)^2
Now, let's solve for u1 and u2 separately by taking the square root of both sides of the equations.
Taking the square root of Equation 1:
sqrt(190) = sqrt((u1)^2)
13.77 = u1
Taking the square root of Equation 2:
sqrt(350) = sqrt((u2)^2)
18.71 = u2
Now we have the speeds corresponding to the given resistance values, u1 = 13.77 km/h and u2 = 18.71 km/h.
To find the speed at which the resistance is 302.5 Newtons, we need to find the square root of 302.5 and solve for u.
sqrt(302.5) = sqrt((u)^2)
17.41 = u
Therefore, the speed at which the resistance is 302.5 Newtons is approximately 17.41 km/h.