Eric is standing on the ground, a distance of 70 ft from the bottom of Ferris wheel that has a 20 ft radius. His arm is at the same height as the bottom of the Ferris wheel. Janice is on Ferris wheel which makes one revolution counter clock wise every 16 secs. At the instant she is at a point A, Eric throws a ball to her at 60 ft/ sec at an angle of 60 degrees above the horizontal.will the ball reach Jenice? Show the equations for the Ferris wheel and the ball and draw the graph.

Question

Eric is standing on the ground, a distance of  70 ft from the bottom of Ferris wheel that has a 20 ft radius. His arm is at the same height as the bottom of the Ferris wheel. Janice is on Ferris wheel which makes one revolution counter clock wise every 16 secs. At the instant she is at a point A, Eric throws a ball to her at 60 ft/ sec at an angle of 60 degrees above the horizontal.will the ball reach Jenice? Show the equations for the Ferris wheel and the ball and draw the graph.
What is the minimum distance between the ball and Janiceon the Ferris wheel and what is the time at which the minimum distance occurs?

Steve · Answer

If Janice is at (0,0) when t=0, then the wheel obeys

w(t) = 20(1-cos(π/8 t))

The ball follows the parametric equations

x(t) = -70 + 60cos60° t
y(t) = 60sin60° t - 16t^2

I have no idea where point A is, but having the equations should make things amenable to solution.

Steve · Answer

Oops. The w(t) given above is the y-value of Janice's position. You also need to use the x-value, which I'm sure you can do.

Praphul · Answer

I need the minimum distance