An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 137 ft at an angle of 31.0° above the horizontal. It then moves 137 ft at an angle of 48.0° below the horizontal. If we take the initial horizontal motion of the car to be along the + x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the + x-axis

Question

Sincere Schmitt

Physics

15 March, 03:14

An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 137 ft at an angle of 31.0° above the horizontal. It then moves 137 ft at an angle of 48.0° below the horizontal. If we take the initial horizontal motion of the car to be along the + x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the + x-axis

+3

Answers (1)

Know the Answer?

Daniel Costa · Answer 1

We know that

Δr = r₁ - r₀

r₀ = 0 i + 0 j

r₁ = (162+137*Cos (31º) + 137*Cos (-48º)) i + (0+137*Sin (31º) + 137*Sin (-48º)) j = (371.1028 i - 31.2506 j) ft

Δr = r₁ - r₀ = (371.1028 i - 31.2506 j) - (0 i + 0 j) = (371.1028 i - 31.2506 j) ft

Magnitude:

Δr = √ ((371.1028) ² + (-31.2506) ²) = 372.4163 ft

Angle:

tan θ = ( - 31.2506 / 371.1028) = - 0.0839 ⇒ θ = tan⁻¹ (-0.0839) = - 4.8135º

(below the horizontal).