Question

5. The merry-go-round at a certain park takes riders on a spin at about 9 m/s. The radius of the circle about which the outside riders move is approximately 8 m. How long does
it take for the outside riders to make one complete cycle.

6. A race car makes 50 revolutions around a circular race track of radius 1000 m every 2 min.

(a) What is the average linear speed of the car as it travels along the track?
(b) What is the car’s centripetal acceleration?

7. A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball drops from 18.3 rads/s to 12.1 rads/s. During the slow-down, the angular displacement is 81.5 rads. How long does it take the ball to stop spinning?

8. A soccer ball is kicked horizontally off a 100-meter high hill and lands a distance of 20 meters from the edge of the hill. What was the initial horizontal velocity of the soccer ball?

9. An quarterback launches a football to a receiver with an initial velocity of 5 m/s.
(a) At what angle must the ball be launched so that it clears the furthest horizontal distance?

(b) How long does it take to clear the furthest horizontal distance?
(c) What is the furthest horizontal distance the ball reaches?
(d) How high did the ball get before heading back down?

Answer 1

5)

Time, t = 2 pi r/v

t = 2 pi x 8/9 = 5.59 sec

6)

A)

Velocity, v = rw = 1000 x (50 x 2 pi/2 x 60) = 2618 m/s

B)

Acceleration, a = w^2r = (50 x 2 pi/2 x 60)^2 x 1000 = 6853.9 m/s^2

7)

w^2 = wo^2 + 2 a theta

12.1^2 = 18.3^2 + 2 x a x 81.5

Angular acceleration, a = - 1.16 rad/sec^2

W = wo + at

0 = 18.3 - 1.16 t

Time, t = 15.8 sec

8)

S = ut + 0.5 at^2

100 = 0 + 0.5 x 9.8 x t^2

Time, t = 4.52 sec

Velocity, v = 20/4.52 = 4.43 m/s

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