the resistance to a motion of a car is partly constant and partly proportional to the square of the speed u. when the speed is 30km/hr the resistance is 190N and when the speed is 50km/hr the resistance is 350N. find what speed the resistance is 302.5N

Answer 1

Let's denote the constant resistance as R and the resistance that is proportional to the square of the speed as k·u², where k is a constant.

Given that when the speed is 30 km/hr, the resistance is 190 N, we can write the equation:

R + k(30 km/hr)² = 190 N

Similarly, when the speed is 50 km/hr, the resistance is 350 N, which gives us the equation:

R + k(50 km/hr)² = 350 N

Subtracting the first equation from the second equation, we get:

k(50 km/hr)² - k(30 km/hr)² = 350 N - 190 N

Simplifying,

k(50² - 30²) = 160

k(2500 - 900) = 160

k(1600) = 160

k = 160 / 1600

k = 0.1

Now we can substitute k into one of the earlier equations to find R:

R + 0.1(30 km/hr)² = 190 N

R + 0.1(900 km²/hr²) = 190 N

R + 90 N = 190 N

R = 190 N - 90 N

R = 100 N

Finally, we can find the speed at which the resistance is 302.5 N:

R + k·u² = 302.5 N

100 N + 0.1u² = 302.5 N

0.1u² = 302.5 N - 100 N

0.1u² = 202.5 N

u² = 202.5 N / 0.1

u² = 2025

Taking the square root of both sides:

u = √(2025)

u ≈ 45 km/hr

Therefore, the speed at which the resistance is 302.5 N is approximately 45 km/hr.