Chapter 4, Problem 95RPP

Professor tests airplane takeoff speed D A Wardle, a professor of physics from the University of Auckland New Zealand tested the takeoff speed of a commercial airliner. The pilot had insisted that the takeoff speed had to be 232 km /h To perform the testing experiment, Wardle used a pendulum attached to stiff cardboard (Figure 4.14) Prior to takeoff, when the plane was stationary, he marked the position of the pendulum bob on the cardboard to provide a vertical reference line (the dashed line in Figure 4.14) During the takeoff, he recorded the position of the bob at 5-s intervals. The results are shown in the table.

The information is taken from the article by D. A Wardle "Measurement of aeroplane takeoff speed and cabin pressure" published in The Physics Teacher, 37, 410-411 (1999).

t( S)	$\theta (°)$
0	9.9
5	14.8
10	13.8
15	13.0
20	12.0
25	11.4

Using these data, Professor Wardle determined the acceleration at takeoff to be greater than g/4. Then he plotted an acceleration-versus-time graph and used it to find the takeoff speed It turned out to be about 201 km /h. He was very satisfied—the day was windy, and the speed of the breeze was about 15-20 km /h Thus the takeoff speed predicted by his simple pendulum was 215-220 km /h very close to what the pilot said.

The professor used which of the following expressions for the pendulum bob acceleration ( $\theta$ is the angle of the pendulum bob string relative to the vertical)?

$\begin{array}{l}\text{a}\text{. }a=g\text{ sin }\theta \\ \text{b}\text{. }a=g\text{ cos }\theta \\ \text{c}\text{. }a=g\text{ tan }\theta \\ \text{d}\text{. None of the choices}\end{array}$