Class Management I Help 2 D & 3_D Motion Begin Date: 2/10/2018 2:01:00 PM Due Da

Question

Class Management I Help 2 D & 3_D Motion Begin Date: 2/10/2018 2:01:00 PM Due Date: 2/17/2018 11:59:00 PM End Date: 2/27/2018 11:59:00 PM (5 %) Problem 11: A jet flying from Cairns, Australia, has an air speed of 264 m/s in a direction 50° south of west. It is in the jet stream, which is blowing at 31 m/s in a direction 15° south of east. In this problem you are going to be asked about the velocity of the airplane relative to the Earth 50% Part (a) What is the magnitude of the velocity of the airplane relative to the Earth in m/s? 50% Part (b) What is the angle of the velocity of the airplane relative to the Earth in degrees? Give the angle S of W Grade Summary Potential Late work % 809 Late Potential 78.4 cos0 cotan asin) tan() ( acos0 sin atan acotan sinh cosh0 tanhO cotanhO Submissions Attempts remaining: (1% per attempt) detailed view 0 Degrees O Radians 1% 1% Submit Hint I give up!

Explanation / Answer

given

air speed of jet, u = 264 m/s
direction, theta = 5 deg south of west

spee do f jet stream, v = 31 m/s
direction, phi = 15 deg south of east

a. velocity of airplane relative to earth = vr
vr = u - v
u = -264(cos(5)i + sin(5)j)
and
v = 31(cos(15)i - sin(15)j)

hence
vr = -233.051699i -31.032506 j m/s

hence
|vr| = 235.108 m/s

b. direction = arctan(31.03/233.05) = 7.584 deg south of west

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