What Is the Takeoff Speed of an Aircraft Based on a Watch's Angle?

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The discussion revolves around estimating the takeoff speed of an aircraft based on the angle of a watch held by a passenger during takeoff. The watch makes a 25° angle with the vertical, leading to the calculation of acceleration using the tangent function, resulting in an acceleration of approximately 4.57 m/s². By applying the formula for velocity, the estimated takeoff speed is calculated to be around 82.2 m/s. This speed translates to approximately 300 km/h, which aligns with realistic takeoff speeds for jetliners. The calculations and conclusions presented confirm the accuracy of the estimated takeoff speed.
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Francesca dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport. She notices that the string makes an angle of 25° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 18s. Estimate the takeoff speed of the aircraft.

k so you know that the force of gravity is mg and it's going down, and that the acceleration is ma along the horizontal, and so can you take the tan(25)=a/9.8 to get an acceleration of 4.57m/s^2?

And so for velocity you would get V=Vo+at
V=0+(4.57)(18)
V=82.2m/s?

thanks for reading
 
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It seems to be correct. Which means the take-off speed is around 300 km/h which is realistic.
 
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