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Chapter 4: Q. 46 (page 107)
A projectile鈥檚 horizontal range over level ground is . At what launch angle or angles will the projectile land at half of its maximum possible range?
The required angles are.
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A Ferris wheel of radius R speeds up with angular acceleration starting from rest. Find an expression for the (a) velocity and (b) centripetal acceleration of a rider after the Ferris wheel has rotated through angle.
6. A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.6 shows graphs of and , the x - and y-components of the puck's velocity. The puck starts at the origin.
a. In which direction is the puck moving at ? Give your answer as an angle from the x-axis.
b. How far from the origin is the puck at ?
15. FIGURE Q4.15 shows a pendulum at one end point of its arc.
a. At this point, is positive, negative, or zero? Explain.
b. At this point, is positive, negative, or zero? Explain.
FIGURE Q4.15
Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is 6.37 * 106 m, and the altitude of a geosynchronous orbit is 3.58 * 107 m (鈮�22,000 miles). What are
(a) the speed and
(b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?
A cannon on a train car fires a projectile to the right with speed , relative to the train, from a barrel elevated at angle . The cannon fires just as the train, which had been cruising to the right along a level track with speed, begins to accelerate with acceleration , which can be either positive (speeding up) or negative (slowing down). Find an expression for the angle at which the projectile should be fired so that it lands as far as possible from the cannon. You can ignore the small height of the cannon above the track.
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