You want to toss an object to a friend who is riding a ferriswheel. The followin

Question

You want to toss an object to a friend who is riding a ferriswheel. The following parametric equations give the path of thefriend R1(t) and path of object R2(t).Distance is measured in meters and time is measured in seconds.

r1(t)=15(sin((Pie*t)/10))i + (16-15(cos((Pie*t)/10))j

R2 (t)= (22-8.03(t-t0))i +(1+11.47(t-t0)- 4.9(t-t0)2)j

question:

a. identify where your friend is at t=0.

b. determine the number of revolutions per minute of the Ferris wheel.

c. find the speed and angle of inclination (in degrees) at which the object is thrown. find the value of t0 in order for your friend to catch the ball, round t0 to the nearest tenth. explain exactly what you should do for your friend to catch the ball.

d. find the approximate time your friend should be able to catch the object. approximate the speed of your friend and the object at that time.

Explanation / Answer

tan() = y/x = dy/dx = dy/dt / dx/dt

dr2x/dt = d/dt[22-8.03(t-t0)] = -8.03
dr2y/dt = d/dt[1 + 11.47(t-t0)- 4.9(t-t0)²]

= 11.47 - 9.8(t-t0)

at t=t0
dr2y/dt = 11.47 - 9.8*0 = 11.47

tan() = dr2y/dr2x = 11.47/(-8.03)
= tan¹(-11.47/8.03)
= -55.0°

|dr2/dt| = [(dr2x/dt)² + (dr2y/dt)²]

= ((-8.03)² + 11.47²)

= 14.0
Thus, the speed is 14.0m/s; the angle is -55.0°, or 55.0° below the horizontal

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