Jean, who likes physics experiments, dangles her watch from a thin piece of stri

Question

Jean, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from Dulles Airport (Fig. 4-55). She notices that the string makes an angle of 24° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 15 seconds. Estimate the takeoff speed of the aircraft.
m/s

Jean, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from Dulles Airport (Fig. 4-55). She notices that the string makes an angle of 24 with respect to the vertical while the aircraft accelerates for takeoff, which takes about 15 seconds. Estimate the takeoff speed of the aircraft.

Explanation / Answer

Draw a free body diagram about the watch.. The horizontal component will equal the mass * acceleration. With the acceleration you can calculate the speed

So summing vertical forces we have T*cos( ) = m*g

so T = m*g/cos()

Now T*sin() = m*a

so m*g*sin()/cos() = m*a

so a = g*tan() = 9.80*tan(24) = 4.36m/s^2

Now v = v0 + a*t = 0 + 4.36m/s^2 * 15s =65.4m/s

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