A pilot takes off from a town in Northern California and aims her airplane due N

Question

A pilot takes off from a town in Northern Californiaand aims her airplane due North toward Seattle with a speed VPW = 240.0 km/h relative to the air. (Subscripts P stand for airplane and W for wind in the air.) The air has an Eastward wind of unknown speed VWE relative to the Earth. (Subscript E stands for Earth.) The airplane lands after flying in the air for 4.00 hours. The airplane’s final destination is a small airport 300 .00 km directly East See diagrams below, showing (i) relevant velocity vectors, (ii) a map-compass, and (iii) the displacements of the airplane after the entire flight, from start, to finishat airport directly East of Seattle.

(a) (10 points) The speed of the wind VWE relative to the Earth.

(b) (10 points) The speed of the airplane VPE relative to the Earth.

(c) (10 points) What is the direction of the airplane’s velocity relative to the Earth? Find this direction by computing the angle this velocity makes with the North direction shown in the schematic of the problem below.

(d) (5 points) What is the distance between the airplane’s startingpoint and Seattle?

(e) (5 points) What is the distance between the starting point and the small airport where airplane lands at spot marked “FINISH” below.

Explanation / Answer

here,

distance to the east , de = 300 km

time taken , t = 4 hours

(a)

The speed of the wind VWE relative to the Earth , VWE = De/t

VWE = 75 km/h

The speed of the wind VWE relative to the Earth is 75 km/h

(b)

The speed of the airplane VPE relative to the Earth , VPE = 75 km/h i + 240 km/h j

The speed of the airplane VPE relative to the Earth , |VPE| = sqrt(75^2 + 240^2)

|VPE| = 251.45 Km/h

The speed of the airplane VPE relative to the Earth is 251.45 km/h

(c)

theta = arctan(75 / 240)

theta = 17.35 degree

the angle is 17.35 degree from the north in clockwise direction

(d)

the distance between the airplane’s startingpoint and Seattle , d = de/tan(theta)

d = 300/tan(17.35)

d = 960.24 km

the distance between the airplane’s startingpoint and Seattle is 960.24 km

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