A 1210-kg car travels up an incline at constant velocity.The incline is 15 $\circ$ measured with respect to the horizontal.The change in the car's potential energy is 1.92 MJ.What is the length of the incline?

Question

Quizplus · Accepted Answer

The change in potential energy (ΔPE) can be calculated using the formula ΔPE = mgh, where m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height gained. Given ΔPE = 1.92 MJ (or 1.92 x 10^6 J) and m = 1210 kg, we can solve for h:1.92 x 10^6 J = 1210 kg * 9.8 m/s^2 * h,h = (1.92 x 10^6 J) / (1210 kg * 9.8 m/s^2) ≈ 160 m.To find the length of the incline (L), we use the trigonometric relation sin(θ) = opposite/hypotenuse, where θ = 10 degrees and the opposite side is the height (h). Thus,sin(10°) = h/L,L = h / sin(10°) ≈ 160 m / sin(10°) ≈ 920 m or 0.92 km.Among the given options, 0.62 km (E) is the closest to the calculated length of the incline.

A 1210-Kg Car Travels Up an Incline at Constant Velocity ∘\circ∘

A 1210-Kg Car Travels Up an Incline at Constant Velocity $\circ$