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SOLUTIONS TO EXERCISE 26
(a) The acceleration described is (75 mph)/(4 sec). Let's convert to meters per second: a = (75 mi/hr)/(4 s) * (1 hr)/(3600 s) * (1609 m)/(1 mi) = 8.4 m/s^2. So the Harley-Davidson's acceleration is 8.4/9.8 = 85 percent that of Earth's gravitational acceleration at the planet's surface. (b) It starts with a downward velocity of zero. Let's round off Earth's gravitational acceleration to 10 m/s^2 for this calculation; so after 4 seconds it will be going (10 m/s^2 * 4 s) = 40 m/s. (c) The Harley's speed has increased smoothly from 0 to 40 m/s during this time; so its average speed was halfway between the starting and ending speed, or 20 m/s. Since it's falled for four seconds, it's traveled r = vt = 20 m/s * 4 s = 80 m. (d) When the Harley is one inch off the ground, we can say it's pretty much right at Earth's surface. So the gravitational force is F = GMm/r2 = m times the gravitational acceleration = 450 kg * 10 m/s^2 = 4500 Newtons. |