Question

Can you help me solve this problem? I really don't know what to do. I solve problems like for example the rate of change of the elevation but I just encountered this kind of problem so I really don't know what to do. Please help me
The endpoints of a movable rod of length 1 meter have coordinates (x,0) and (0,y). The position of the end on the x-axis is x(t)= (3/5) sin (pi*t) where t is time in seconds.
a) Find the time of 1 complete cycle of the rod.
b) What is the lowest point reached by the end of the rod on the y-axis?
c) Find the speed of the y-axis endpoint when the x-axis endpoint is (3/10, 0)

Answer 1

(a) the period of sin(kt) is 2π/k, so we have period 2π/π = 2 seconds.

(b) since the minimum of sin(kt) = -1, our minimum is -3/5

(c) since the length of the rod is 1,
x^2+y^2 = 1
That means that
y^2 = 1/25 (16 + 9cos^2(πt))

when x = 3/10, t=1/6, y = √91/10

Now, we know that

2y dy/dt = 1/25 (-9πsin(2πt))
so,
dy/dt = -(9π√3)/(10√91)
As expected, it is falling, if the x end is moving right.