Question

1 In a disastrous first flight, an experimental paper airplane follows the trajectory indicated by these parametric equations: x(t) = 1 - 3 sint y(t) = 4 - 3 cost but crashes into a wall after 10 seconds. Give all coordinates as (x,y) coordinates, along with their associated t values. The (x,y) simply gives you the location of the plane. The x-axis can be assumed to be the ground. You could consider the y values to be in feet, so the y values are distance from the ground, so they will never be negative. But the x values are just coordinates and could be positive or negative - the y-axis is not a wall- consider it to be invisible and not a barrier. Write all decimals to two decimal places. (a) Find (b) Find all the vertical tangents, if any. Explain by testing the change in signs of the derivative. (c) Find all the horizontal tangents, if any. Explain by testing the change in signs of the derivative. (d) Use the results of (b) and (c) to indicate on which t intervals the x values are increasing and decreasing, and on which t intervals the y values are increasing and decreasing. (e) Find and do the Test For Concavity. Indicate on what t intervals the graph is concave up and on which t intervals it is concave down. (f) Sketch the graph over the time interval from 1 = 0 to 1 = 10- don't forget to include arrows. Clearly indicate where the plane is first thrown as an (x,y) coordinate and where the plane hits the wall as an (x,y) coordinate. You can estimate where the y-intercepts are.

Answer 1

Chegg rules i posted five subparts

Answer: The Given information is MU)-t-3 Sint YCU)=4-3 Cost a) dyldt doldt dox da dt 21-3 Cost dy = 3 Sint dt (dy da 3sint 1-3cost + 3 Sint de la C), dal - 1- 3 cost dt do dt 1-3cost=0 (cost=-3 " If t value value 2 o to z if decreasing to show if increasing asint cott comm] decreasing cott L.]. Incoreasing d621 ,2 del = 3 cost 3 cost - cott dai 3 sint ld y cott dy