Please show work A commuter airplane starts from an airport and takes the route
ID: 2113935 • Letter: P
Question
Please show work
A commuter airplane starts from an airport and takes the route shown in Figure P3.19. The plane first flies to city A, located 175 km away in a direction 30.0degree north of east. Next, it flies for 150 km 20.0degree west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C 'relative to the location of the starting point. A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in Figure P3.58. If he shoots the ball at a 40.0degree angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m.Explanation / Answer
OA vector = 175 cos 30i + 175 sin 30 j
AB vector = -150 cos 70i + 150 son 70 j
BC vector = -190 i
so, OC = OA + AB + BC
=( 175 cos 30 - 150 cos 70 - 190 ) i + ( 175 sin 30 + 150 sin 70 ) j
= -89.7486 i + 228.454 j^
so ... distance of C from O =
sqrt ( 89.7486^2 + 228.454^2 )
= 245.451 Kms
direction = tan inverse ( 228.454 / 89.7486 ) = 68.5525 west of north