Respuesta :
Answer:
a) R = 186.742 ft
b) θ = 0.7854 rads
c) θ = 14.14 rads
Explanation:
Given:
- The linear tangential velocity v = 200 mph
- The angular frequency a = 15 RPM
- The distance of bottom point from ground c = 3 ft
Find:
- The radius R of the ferris wheel
-Once the wheel is built, John suggests that Tiff should take the first ride. The wheel starts turning when Tiff is at the location P, which makes an angle θ with the horizontal, as pictured. It takes her 1.5 seconds to reach the top of the ride. Find the angle θ. (Round your answer to two decimal places.)
- Poor engineering causes Tiff's seat to fly off in 9 seconds. Describe where Tiff is located (an angle description) the instant she becomes a human missile. (Give your answer as an angle measured counterclockwise from her starting point P.)
Solution:
- The relationship between linear v and rotational speed w is given by:
v = R*w
200*5280 / 60 = R*15*2*π
R = 200*5280 / 60*15*2*π
R = 186.742 ft
- the angle swept from point P to angle θ above horizontal is given in terms of angular speed:
π/2 + θ = a*2π*1.5 / 60
θ = 15*2π*1.5 / 60 - π/2
θ = 0.7854 rads
- Similarly calculate the angle θ swept entirely till 9 seconds
θ = a*2π*9 / 60
θ = 15*2π*9 / 60
θ = 14.14 rads
- The total angle swept from initial position is θ = 14.14.
