Jean dangles her watch from a thin piece of string while the jetliner she is in takes off. She notices that the string makes an angle of 22° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 18 seconds. Estimate the takeoff speed of the aircraft.

tan22=ma/mg= a/g

a= g tan22

You know acceleration.

vf= at you know a, time t.

oh, thank you. I forgot to do that after my calc homework

I keep getting Vf= 1.56 m/s which webassign says is wrong. It's in the chapter about Newtons laws of motion so, even though it is not included in the question, could that have a bearing on my answer, and if so how?

It would help if you put your calculator in degrees, and worked with 22 degrees, not 22 radians. Goodness.

To estimate the takeoff speed of the aircraft, we can use the concept of forces and acceleration in the vertical direction.

First, let's understand the situation. Jean dangles her watch from a thin piece of string during takeoff. The angle between the string and the vertical direction is given as 22°. This angle is related to the acceleration experienced by Jean and her watch.

The force causing the change in direction of the string is the net force acting on the watch. This force can be decomposed into two components: the tension in the string and the gravitational force acting on the watch.

The tension in the string can be considered the vertical component of the net force, while the gravitational force is the horizontal component. The vertical component causes the watch to hang at an angle, and the horizontal component tries to pull it away sideways.

Since the watch is in equilibrium, the net force acting on it is zero. This means that the vertical component of the net force must be equal to the weight of the watch.

Let's denote the takeoff speed of the aircraft as v, and the time for takeoff as t.

Now, we can use the concept of acceleration to relate the angle and the takeoff speed of the aircraft. The vertical component of the acceleration is g, the acceleration due to gravity.

sin(22°) = (g * t) / v

Rearranging the equation, we can solve for v:

v = (g * t) / sin(22°)

To calculate the takeoff speed, we need the value for g, the acceleration due to gravity. On Earth, g is approximately 9.8 m/s^2.

Let's substitute the values:

v = (9.8 m/s^2 * 18 s) / sin(22°)

Calculating this equation will give you an estimate of the takeoff speed of the aircraft.