Physics Help Plss?

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 25° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 16 seconds. Estimate the takeoff speed of the aircraft.

Answer 1

http://en.wikipedia.org/wiki/Acceleration

Answer 2

EDIT*Jessie, you should use cot(25), not tan(25)*

We can use this information to determine the acceleration of the airplane during takeoff (assuming it's constant).

|_\
|25\
|____\
|______\
|________\
|__________\ <---Watch

The string has a tension (which runs up the hypotenuse of the right triangle above).

So, we can break it into components.


In the y-direction
T sin(25) = mg

In the x-direction
T cos(25) = ma


Solving the first equation for T yields
T = 23.189 * m

Substituing this into the second equation,

T cos(25) = ma
(23.189 * m) * cos(25) = ma

The m's divide out, giving
a = 21.016 m/s/s

Since vf = vi + a*t, and vi = 0 (the plane started from rest), we have

vf = a*t = 21.016 * 16 = 336.259 m/s

Rounding to 2 sig figs, vf = 340 m/s

Answer 3

v=g X tan (angle) X time

v= 9.81 X tan (25) X 16

V=73.19