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- A spacecraft lands on a newly discovered planet orbiting the star 51 Pegasi. To measure the acceleration from gravity on the planet, an astronaut drops a rock from a height of 2 m. A precision timer indicates that it takes the rock 0.71 s to fall to the surface. What is the acceleration from gravity on this planet?The average person passes out at an acceleration of 7g (that is, seven times the gravitational acceleration on Earth). Suppose a car is designed to accelerate at this rate. How much time would be required for the car to accelerate from rest, to 60.0 miles per hour? (The car would need rocket boosters!)A seagull flies at a velocity of 9.00 m/s straight into the wind. (a) If it takes the bird 20.0 min to travel 6.00 km relative to the Earth, what is the velocity of the wind? (b) If the bird turns around and flies with the wind, how long will he take to return 6.00 km? (c) Discuss how the wind affects the total round-trip time compared to what it would be with no wind.
- Consider a grey squirrel falling out of a tree to the ground. (a) If we ignore air resistance in this case (only for the sake of this problem), determine a squirrel's velocity just before hitting the ground, assuming it fell from a height of 3.0 m. (b) If the squirrel stops in a distance of 2.0 cm through bending its limbs, compare its deceleration with that of the airman in the previous problem.The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of power roller skates, which provide a constant horizontal acceleration of 15.0 m/s2, as shown in Figure P3.59. The coyote starts off at rest 70.0 m from the edge of a cliff at the instant the roadrunner zips in the direction of the cliff, (a) If the roadrunner moves with constant speed, find the minimum speed the roadrunner must have to reach the cliff before the coyote. (b) If the cliff is 1.00 102 m above the base of a canyon, find where the coyote lands in the canyon. (Assume his skates are still in operation when he is in flight and that his horizontal component of acceleration remains constant at 15.0 m/s2.) Figure P3.59A hard rubber ball, released at chest height, falls to the pavement and bounces back to nearly the same height. When it is in contact with the pavement, the lower side of the ball is temporarily f fattened. Suppose the maximum depth of the dent is on the order of 1 cm. Find the order of magnitude of the maximum acceleration of the ball while it is in contact with the pavement. State your assumptions, the quantities you estimate, and the values you estimate for them.
- A basketball player dribbles the ball while running at a constant speed straight across the court. Think about the velocity and acceleration of the ball and then sketch a motion diagram for the ball. Explain how you arrived at your sketch.An ice sled powered by a rocket engine sum from rest on a large frozen lake and accelerates at + 40 ft/s2. After some time t1, the rocket engine is shut down and the sled moves with constant velocity v for a time t2. If the total distance traveled by the sled is 17 500 ft and the total time is 90 s. find (a) the times t1 and t2 and (b) the velocity v. At the 17 500-ft mark, the sled begins to accelerate at 20 ft/s2. (c) What is the final position of the sled when it comes to rest? (d) How long does it take to come to rest?A hockey puck struck by a hockey stick is given an initial speed v0 in the positive x-direction. The coefficient of kinetic friction between the ice and the puck is k. (a) Obtain an expression for the acceleration of the puck. (b) Use the result of part (a) to obtain an expression for the distance d the puck slides. The answer should be in terms of the variables v0, k, and g only.
- A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the trip. (b) Determine the distance between the initial and final cities along the route.A woman is reported to have fallen 144 ft from the 17th floor of a building, landing on a metal ventilator box that she crushed to a depth of 18.0 in. She suffered only minor injuries. Ignoring air resistance, calculate (a) the speed of the woman just before she collided with the ventilator and (b) her average acceleration while in contact with the box. (c) Modeling her acceleration as constant, calculate the time interval it took to crush the box.4. Which of the following sentences describes an example of instantaneous velocity? A.The hot-air balloon rose upward 42 meters in 12 seconds. B. The pitcher can throw a baseball that moves at 42 meters per second. C. The runner moved 18 kilometers in her first 2 hours of the marathon. D. At the 10-second mark, the submersible was sinking downward at 25 meters per second.