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A truck travels beneath an airplane that's moving 200 km/h at an angle of 21 degrees to...

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fieldsofwheat | Student, Undergraduate | eNoter

Posted October 15, 2011 at 3:39 AM via web

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A truck travels beneath an airplane that's moving 200 km/h at an angle of 21 degrees to the ground. How fast must the truck travel to stay beneath the airplane?

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fieldsofwheat | Student, Undergraduate | eNoter

Posted October 15, 2011 at 3:40 AM (Answer #1)

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BTW, also, what's the magnitude of the vertical component of the velocity of the plane? Answer in units of km/h

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted October 15, 2011 at 4:51 AM (Answer #2)

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The airplane is traveling at 200 km/h and its velocity makes an angle of 21 degrees to the ground. The velocity of the airplane can be divided into a horizontal and a vertical component.

The magnitude of the vertical component of the velocity of the airplane is equal to 200*sin 21 = 71.67 km/h

The magnitude of the horizontal component of the airplane's velocity is given by 200*cos 21 = 186.71 km/h

For the truck to always remain under the aircraft only the horizontal component of the velocity matters as irrespective of how high the airplane goes the truck will remain under it.

Therefore the truck should travel at 186.71 km/h in the direction of the horizontal component of the airplane's velocity to always remain under it.

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