On her flight home at Thanksgiving, Margaret decides to apply the physics she ha

Question

On her flight home at Thanksgiving, Margaret decides to apply the physics she has learned in PHYC1300 to measure the speed of the aircraft when it takes off. She dangles her watch from a string while the aircraft accelerates down the runway. Draw a free body diagram of the watch. Using her protractor, she notices that the string makes an angle of 20° with respect to the vertical edge of the window as the aircraft accelerates on the runway, which takes about 26 s. Estimate the takeoff speed of the aircraft.

Explanation / Answer

Write the horizontal and vertical components of force are

Fx = ma - T sin 20° = 0
Fy = mg - T cos 20° = 0

From the second equation, the tension,

T = mg / cos 20°

Substitute this into the first equation

ma = [ mg / cos 20° ] sin 20° = mg tan 20°

Solve for aceeleration

a = g tan 20° = 3.5669 m/s2

Use constant acceleration equation; the velocity is found from

v = at = ( 3.5669 m/s2 ) ( 26 s ) = 92.7 m/s

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