The resistance R to the motion of a car is partly constant and partly varies as the square of the speed V. At 80km/hr the resistance is 1060N and at 120km/hr, its resistance is 1460N. What will be the resistance at 140km/hr
The resistance r to the motion of a car is partly constant and partly proportional to the square of the speed v. When the speed is 30km/h, the resistance is 190 newtons and when the speed is 50km/h, the resistance is 350 newtons. Find for what speed the resistance is 302.5 newtons
R = ks^2+m
1060 = (80*80)k+m
6400k+m = 1060 ........(i)
1460 = (120*120)k+m
14400k+m = 1460 .........(ii)
Solve i and ii simultaneously and get k and m.
At 140km/h,
R = (140*140)k+m
Substitute for k and m and get the resistance at 140km/h
My answer is 0
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A varies darectly as M and N inversely as the square root of V.the relationship between A,M,N,V solution AXMN/V" A=KMN/V"
Well, let me do some calculations and try to resist being funny for a moment.
Let's call the constant part of the resistance "C" and the variable part "kV^2". We know that at 80 km/hr (or 22.22 m/s), the resistance is 1060 N, and at 120 km/hr (or 33.33 m/s), the resistance is 1460 N.
So we can set up two equations based on the given information:
1060 = C + k(22.22)^2
1460 = C + k(33.33)^2
Now, let's solve these equations to find the values of C and k, and then we can find the resistance at 140 km/hr (or 38.89 m/s).
Ready? Now, it's time for the suspenseful moment where I calculate the results...
After performing the math wizardry, I find that C ≈ 697.09 N and k ≈ 0.01138 N/s^2.
Now, let's plug in the value of V = 38.89 m/s into the equation:
Resistance at 140 km/hr = C + k (38.89)^2
Resistance at 140 km/hr ≈ 697.09 + 0.01138(38.89)^2
And the final resistance at 140 km/hr is approximately... drumroll, please... 1752.63 N.
To find the resistance at 140 km/hr, we need to determine the constant and variable components of the resistance R.
Let's denote the constant component as C and the variable component as V^2, where V is the speed.
From the given information, we know that at 80 km/hr, the resistance is 1060 N, and at 120 km/hr, the resistance is 1460 N.
Using this information, we can set up two equations:
1) At 80 km/hr: R = C + (80)^2
2) At 120 km/hr: R = C + (120)^2
Substituting the given resistance values into the equations, we get:
1) 1060 = C + (80)^2
2) 1460 = C + (120)^2
Simplifying the equations:
1) C = 1060 - 80^2
2) C = 1460 - 120^2
Now let's solve for the constant component C:
1) C = 1060 - 6400
2) C = 1460 - 14400
1) C = -5340
2) C = -12940
Since resistance cannot be negative, we can disregard C = -5340.
Therefore, the value of the constant component C is C = -12940.
To find the variable component V^2 at each speed, we substitute the values into one of the original equations:
1) At 80 km/hr: R = -12940 + (80)^2
R = -12940 + 6400
R = -6540
2) At 120 km/hr: R = -12940 + (120)^2
R = -12940 + 14400
R = 14560
Now, we have the equation representing the variable component of the resistance: V^2.
To find the resistance at 140 km/hr, we substitute V = 140 into the equation:
R = -12940 + (140)^2
R = -12940 + 19600
R = 6652
Therefore, the resistance at 140 km/hr is 6652 N.