Calculating acceleration?

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. She notices that the string makes an angle of 27° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 20 seconds. Estimate the takeoff speed of the aircraft.

Answer 1

The velocity of the jetliner considering it was acceleration with constant acceleration during time t is
V=at
Acceleration can be found from the relationship between the force of gravity (W=mg) and acceleration the jetliner transfers on to the watch (F=ma). It the ration between two forces
tan(27)=F/W
tan(27)=ma/mg=a/g
a=gtan(27)

so finally
V= g tan(27) t
V= 9.81 tan(27) 20
V=100 m/s (360 km/h)

Answer 2

the acceleration can be found using trig components of the forces on the watch. Remember that Force is mass times acceleration.

The string by with the clock dangles is the hypotenuse (sp?) of a right triangle. The resulting forces from the horizontal and vertical forces is in the tension in this string, but that isnt important. We need to find the Horizontal force on the watch. Instead of using forces, in fact, we can use accelerations. Because mass times acceleration is force and the mass of the clock is always consistent, its mass is negligable. (i dont know how to show you that in a formula, but it is... if you multiply the accelerations by the mass you get the same triangle.. just on a larger scale).

Anyway.. back to the triangle. The vertical force is 9.8 because that is the force of gravity. The angle theta in the picture is represented by "c". I am going to use that angle because it is easier to look at in this picture on Yahoo Answers.. but it IS NOT 27 degrees, it is the compliment... 63 degrees (the angle to the horizontal). The 27 degree angle is the top angle (to the vertical). It doesn't matter which we use, they will give the same answer when we solve the triangle.

|\
| \
|_c\

So we need the adjacent force to "c" (the horizontal force) and we know the opposite force. Our function is then going to be Tangent. (Tangent = O/A)

X is the unknown acceleration

Tangent (63) = 9.8 / X

X = 9.8 / Tangent (63)

X = 9.8 / 1.9622

X = 5 m/s/s

Acceleration multiplied by time is velocity.... 20 times 5 is 100.. the plane is going 100 m/s

Answer 3

did you forget to tell us the length of the piece of string?
that would give us the hypotenuse for which we can employ trig and then solve.