Math  /  Calculus

Question(II) A car drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 125 m . At the very bottom, the normal force on the driver is twice his weight. At what speed was the car traveling?

Studdy Solution
Solve for the speed of the car:
- Cancel m m from both sides of the equation:
g=v2r g = \frac{v^2}{r}
- Solve for v2 v^2 :
v2=gr v^2 = gr
- Substitute the known values (g=9.8m/s2 g = 9.8 \, \text{m/s}^2 and r=125m r = 125 \, \text{m} ):
v2=9.8×125 v^2 = 9.8 \times 125
- Calculate v v :
v=9.8×125 v = \sqrt{9.8 \times 125} v1225 v \approx \sqrt{1225} v35m/s v \approx 35 \, \text{m/s}
The speed of the car was approximately:
35m/s \boxed{35 \, \text{m/s}}

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