The stopping distance of the car when the road slopes at 17⁰ is 128.7 ft.
The given parameters;
speed of the car, v = 60 mi/h
distance traveled on a level roadway = 123 ft
the sloping angle of the new road, Ф = 17⁰
A simple sketch of the problem is given below;
start-------------123ft--------------------end
17⁰ ↓
↓
↓
↓new end due to the given slope
A straight line joining the start and the new end point forms a hypotenuse of the triangle and it will be equal to the new stopping distance of the car.
Apply trigonometry ratio concept to determine the new stopping distance;
[tex]cos (\theta ) = \frac{adjacent}{hypotenuse} \\\\cos(17) = \frac{123 \ ft}{new \ stopping \ distance} \\\\new \ stopping \ distance = \frac{123 \ ft}{cos(17)} \\\\new \ stopping \ distance = \frac{123 \ ft}{0.956} \\\\new \ stopping \ distance = 128.7 \ ft[/tex]
Thus, the stopping distance of the car when the road slopes at 17⁰ is 128.7 ft.
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