Question

I need help answering each part of the question, step by step. I'm a little lost and need clarification. Thank you very much.

A helicopter pilot at an airport is told to fly a distance, d at a speed v directly east to pick up a
stranded hiker. However, he sees no hiker when he arrives. Radioing the control tower, he learns
that the hiker is actually a distance, d west of the airport. The pilot turns around and heads straight
for the hiker at a speed that is 50% faster than his speed during the initial segment of his wrong way
trip.

a. Assume the x-axis points east and has its origin at the airport. Draw a diagram representing the
motion during the trip, indicating the position of the airport, the turning point, and the
rendezvous location. Label the east and westward segments with appropriate symbols and
indicate how those symbols are related to the given information, d and v.
b. What is the average speed of the helicopter during the trip from takeoff to rendezvous with
the hiker?
c. What is the x-component of the helicopter’s average velocity for the trip from takeoff to
rendezvous with the hiker?
d. What is the average velocity of the helicopter in vector notation?

5. A helicopter pilot at an airport is told to fly a distance, d at a speed v directly east to pick up a stranded hiker. However, he sees no hiker when he arrives. Radioing the control tower, he learns that the hiker is actually a distance, d west of the airport. The pilot turns around and heads straight for the hiker at a speed that is 50% faster than his speed during the initial segment of his wrong way trip a. Assume the x-axis points east and has its origin at the airport. Draw a diagram representing the motion during the trip, indicating the position of the airport, the turning point, and the rendezvous location. Label the east and westward segments with appropriate symbols and indicate how those symbols are related to the given information, d and v. b. What is the average speed of the helicopter during the trip from takeoff to rendezvous with the hiker? c. What is the x-component of the helicopter's average velocity for the trip from takeoff to rendezvous with the hiker? d. What is the average velocity of the helicopter in vector notation?

Answer 1

1. 
   a) first it travel towards turning point with v then it return towards origin of west with 1.5v (50% faster) b) Average speed = total distance travelled/time taken time taken to travel to east (turning point) t_1 = d/v time taken for return to west (Rendezvous location) t_2 = 2d/1.5 v = 4d/3v therefore total time = t_1 + t_2 = d/v + 4d/3v t = 7d/3v total distance travelled = 3d \r\n therefore average speed = 3d/7d/3v = 9v/7 c) Average velocity = displacement between initial & final position/time taken Displacement = final position - initial = -d - 0/7d/3v (-ve due to final position in -ve x-axis) Average velocity = -3v/7 Here helicopter travel only in x-direction (east & west) so average velocity = -3v/7 d) v^vector = -3v/7 i^^