At a county fair, a boy and two friends bring their teddy bears on the giant Fer

Question

At a county fair, a boy and two friends bring their teddy bears on the giant Ferris wheel. The boys are seated in positions 45  from each other.  Boy 3  is ahead of boy 2  who is ahead of boy 1 . The wheel has a diameter of 16.7m , the bottom of the wheel is 2.63m  above the ground and its rim is moving at a speed of 1.95m/s . When the wheel brings the second boy to the maximum height (so boy 3  is already on the way down and boy 1  is still on the way up), they all drop their stuffed animals. How far apart will the three teddy bears land?

Explanation / Answer

Bear 1: h = 2.63m + 16.7m/2 + 16.7m/2 * sin45 = 16.88m
Initial vertical velocity = Vo = 1.95m/s * sin(-45) = -1.38 m/s
h = Vo*t + 0.5*a*t^2
-16.88 = -1.38 * t - 0.5*9.8m/s^2*t^2 = -1.38t - 4.9t^2
for t in seconds
quadratic, solve for t = 1.7205 s
Now (finally) we can get the horizontal displacement:
x = Xo + Vo*t + 0.5*a*t^2 = (16.88m/2)*cos45 + (1.95m/s)*cos(45)*1.7205s + 0
(there is no horizontal acceleration)
x =8.38m

Bear 2: h = 2.63m + 16.7m = 19.33m
Initial vertical velocity = Vo = 0
h = Vo*t + 0.5*a*t^2
-19.33 = 0 - 0.5*9.8m/s^2*t^2 = - 4.9t^2
t = sqrt(19.33/4.9) s = sqrt(3.94) s = 1.98 s
(good -- should take longer than the first bear!)
Now (finally) we can get the horizontal displacement:
x = Xo + Vo*t + 0.5*a*t^2 = 0 + (1.95m/s)*1.98s + 0
(there is no horizontal acceleration and no initial horizontal displacement)
x = 3.861m

Bear 3: h = 2.63m + 16.7m/2 + 16.7m/2 * sin135 = 16.88m
Initial vertical velocity = Vo = 1.95m/s * sin45 = 1.38 m/s
h = Vo*t + 0.5*a*t^2
-16.88 = 1.38 * t - 0.5*9.8m/s^2*t^2 = 1.38t - 4.9t^2
for t in seconds
quadratic, solve for t
a= 4.9
b= -1.38
c= -16.88
t = (-b +- sqrt(b^2 - 4ac) ) / 2a
t= 2.0022 s
(good -- should take longer than first bear, as it heads up at first)
Now (finally) we can get the horizontal displacement:
x = Xo + Vo*t + 0.5*a*t^2 = (16.7m/2)*cos135 + (1.95m/s)*cos(45)*2.0022s + 0
(there is no horizontal acceleration)
x = -5.90m + 2.76m = -3.14 m

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