Two-Dimensional Motion

Problems
in
Projectile, Pendulum, Planetary and Circular Motion

Solve all problems on a separate sheet of paper. Use proper problem-solving techniques throughout. You must show all work, including equations, substitutions, and units. Consult your Reference Tables freely.

1.  A bullet fired horizontally from the top of a building has a muzzle velocity of 500. meters per second. A similar bullet dropped from the top of the same building takes 4.00 seconds to reach the ground. How far forward does the first bullet go before it hits the ground?

2.  A ball is thrown horizontally from the roof of a building at a speed of 20. meters per second and hits the ground 3.0 seconds later. (A) Create a table comparing distance of fall versus time for each 0.5 second of the ball's trip.
(B) In a column parallel and adjacent to the table created in part (A), show how far forward (horizontally) the ball moved during each 0.5 second of the ball's trip.(C) Prepare a graph of vertical distance (altitude: y-axis) versus horizontal distance (range: x-axis) illustrating the trajectory of the ball. Use the same scale factor for both axes.

3.  A projectile is shot upward at a 60-degree angle with the horizontal ground and a speed of 200 meters per second. (A) Calculate the horizontal and vertical components of the projectile's velocity. (B) Calculate how far forward (down-range) the projectile has traveled at the end of 4.00 seconds. (C) Calculate the altitude of the projectile after 4.00 seconds of travel.

4.  A stone attached to a string 2.0 meters long is whirled in a horizontal circle. Calculate the speed at which the stone must move for its centripetal acceleration to equal the gravitational acceleration (g) at sea level.

5.  A toy electric train moving at a constant speed on a circular track that has a radius of 1.0 meter travels around the track every 10. seconds. Calculate the centripetal acceleration of the train.

6.  An airplane flying at a constant speed in a circular course of radius 5000. meters is observed to complete each round trip in exactly 400.0 seconds. (A) Calculate the speed of the airplane. (B) Calculate the centripetal acceleration of the airplane.

7.  Calculate the period of a pendulum which possesses a length of 0.098 meters.

8.  Calculate the length of a pendulum which possesses a period of exactly 1.00 seconds.

9.  A satellite is launched into an orbit of radius 3.00 x 10exp12 meters from the center of the Sun. Based on your knowledge of gravitation, circular motion, and Kepler's Third Law, predict the period of the satellite's motion.

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