An analysis of a moving vehicle reveals that resistance to motion is partially constant and partially variable to the square of the speed. At 120km per hour the resistance is 1460 Newton's and at 80km per hour the resistance is 1060 Newton's. Calculate the resistance at a speed of 140km per hour
Let R = resistance, C = constant part of resistance, V = variable part of resistance, and S = speed.
We are given the following:
R = C + V(S^2)
At 120 km/hr:
R1 = 1460 N
S1 = 120 km/hr
At 80km/hr:
R2 = 1060 N
S2 = 80 km/hr
We can set up two equations with these values:
(1) 1460 = C + V(120^2)
(2) 1060 = C + V(80^2)
First, we can solve for C in the second equation:
C = 1060 - V(80^2)
Now, substitute this value of C in the first equation:
1460 = (1060 - V(80^2)) + V(120^2)
Rearrange the equation to solve for V:
V(120^2) - V(80^2) = 1460 - 1060
=> V(14400 - 6400) = 400
=> V(8000) = 400
=> V = 400 / 8000
=> V = 1/20
Now, plug the value of V back into the equation for C:
C = 1060 - (1/20)(80^2)
C = 1060 - (1/20)(6400)
C = 1060 - 320
C = 740
Now we have the values for C and V. To find the resistance at 140 km/hr:
R_new = C + V(S_new^2)
R_new = 740 + (1/20)(140^2)
R_new = 740 + (1/20)(19600)
R_new = 740 + 980
R_new = 1720 N
So, the resistance at a speed of 140 km/hr is 1720 Newtons.