Question

An engineer designs a roller coaster so that a car travels horizontally for 172ft, then cimbs 147ft at an angle of 34.04 above the horizontal. It then moves 147 it at an angle of 43.0∘

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 magnitide of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterciockwise from the + x axis.) magnitude ft direction * counterclockwise from the +x-axis

Answer 1

To find the car's displacement, we need to break down its motion into horizontal and vertical components. The car's displacement is the vector sum of these components. We can calculate the direction of the displacement using trigonometry.

Step-by-step explanation:

To find the car's displacement, we need to break down its motion into horizontal and vertical components. First, we can find the horizontal displacement by using the given value of 172 ft. Next, we can find the vertical displacement by adding the distances climbed and descended, which are both given as 147 ft. The car's displacement is then the vector sum of these two components, which we can find using the Pythagorean theorem. Finally, we can find the direction of the displacement by using trigonometry to calculate the angle between the displacement vector and the +x-axis.