Question

In a disastrous first flight, an experimental paper airplane follows the trajectory of the particle in Example 1:
x = t − 3 sin t, y = 4 − 3 cost (t ≥ 0)
but crashes into a wall at time t = 10 (Figure 10.1.11).
(a) At what times was the airplane flying horizontally?

Answer 1

The airplane was flying horizontally at those times when dy/dt = 0 and
dx/dt = 0. From the given trajectory we have
dy/dt = 3 sin t and
dx/dt = 1 − 3 cos t (6)
Setting dy/dt = 0 yields the equation 3 sin t = 0, or, more simply, sin t = 0. This equation
has four solutions in the time interval 0 ≤ t ≤ 10:
t = 0, t= π, t = 2π, t = 3π


I want to know how do they came up with these four solutions, I solved but I got only 1 t=0

Answer 2

Do you understand how they got to sin(t)=0?

Answer 3

Yes! so t = arcsin(0) = 0 first answer, but I dont understand how did they get the rest of the three answers

Answer 4

The function of sin(t) intercepts the x-axis at \[\pi n\]where n is any real number so you just keep on solving until the value of n*pi surpasses 10 in order to find the zeros.

Answer 5

Thank you! Medal for you!

Answer 6

No problem :p

Answer 7

I have never tried a parametric plot using Mathematica. Des the attachment depict the flight path?

Answer 8

Yes, exactly Robtobey, that is exactly the curve depicted by the parametric equations.

Answer 9

Thank you for your response.