Question

Francesca, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from Dulles Airport. She notices that the string makes an angle of 25° with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18s. Estimate the takeoff speed of the aircraft.

Answer 1

Answer:

$v_f = 82.3 m/s$

Explanation:

When a suspended string makes and angle of 25 degree while aircraft is accelerating on runway then we can use force equations to find the acceleration of the aircraft

So we will have

$T sin\theta = ma$

$T cos\theta = mg$

now from above two equations we have

$a = g tan\theta$

$a = (9.81) tan25$

$a = 4.57 m/s^2$

now if it took 18 s to take off we can have final speed of the aircraft given by

$v_f - v_i = at$

$v_f - 0 = (4.57)(18)$

$v_f = 82.3 m/s$