1. A racquetball is hit straight upward with an initial velocity of 222m/s. The mass of a racquetball is approximately 0.04270.04270.0427 kg. Air resistance acts on the ball with a force numerically equal to 0.5v, where v represents the velocity of the ball at time t. a. Find the velocity of the ball as a function of time. b. How long does it take for the ball to reach its maximum height? c. If the ball is hit from an initial height of 111 meter, how high will it reach?
1. A racquetball is hit straight upward with an initial velocity of 222m/s. The mass of a racquetball is approximately 0.04270.04270.0427 kg. Air resistance acts on the ball with a force numerically equal to 0.5v, where v represents the velocity of the ball at time t.
a. Find the velocity of the ball as a function of time.
b. How long does it take for the ball to reach its maximum height?
c. If the ball is hit from an initial height of 111 meter, how high will it reach?
2. The weight of a penny is 2.52.52.5 grams, and the upper observation deck of the Empire State Building is 369369369 meters above the street. Since the penny is a small and relatively smooth object, air resistance acting on the penny is actually quite small. We assume the air resistance is numerically equal to 0.0025v0.0025?0.0025v. Furthermore, the penny is dropped with no initial velocity imparted to it.
a. Set up an initial-value problem that represents the falling penny.
b. Solve the problem for v(t)?(?)v(t).
c. What is the terminal velocity of the penny (i.e., calculate the limit of the velocity as ?t approaches infinity)?
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