A plane takes off from an airport and flies to town A, located d1 - 260 km from

Question

A plane takes off from an airport and flies to town A, located d1 - 260 km from the airport in the direction 20.00 north of east. The plane then flies to town B, located d2 - 235 km at 30.0° west of north from town A. Use graphical methods to determine the distance and direction from town B to the airport. (Enter the distance in km and the direction in degrees south of west.) distance You will need to make a scale drawing of the plane's motion. One vector will go from the airport to town A, a second from town A to town B, and the displacement vector from town B to the airport. Choose a convenient length scale, and use a protractor for the angles. Measure the length of the displacement vector, and convert using your scale factor. km direction o south of west Need Help? ReadIt + 0/2 points| Previous Answers SerPSE10 3.3.P010 My Notes Ask Your Teacher An engineer designs a roller coaster so that a car travels horizontally for 192 ft, then climbs 117 ft at an angle of 31.0° above the horizontal. It then moves 117 ft at an angle of 40.0° 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.) magnitude The magnitude of the displacement is the length of the vector which goes from the starting point to the ending point. You will need to measure this distance, and multiply by your scale factor. ft direction o counterclockwise from the +x-axis Need Help? ReadIt

Explanation / Answer

d1 = 260(cos20i + sin20j) = 244.32i + 88.93j km

d2 = 235(-sin30i + cos30j = -117.5i + 203.5j km

From airport to B, r = d1+d2

So from B to airport, r = -(d1 + d2)

r = - 126.82i - 292.44 j

Distance = sqrt[ 126.82^2 + 292.44^2] = 319 km

Direction = tan^-1[292.44/126.82] = 66.6 deg.

———————————————————————

R = 192i + 117(cos31i + sin31j) + 117(cos40i - sin40j)

R = 381.92i - 14.95j

Magnitude = 382.2 ft.

Direction = 360 - tan^-1(14.95 / 381.92) = 358 deg  

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