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What Launch Angle Produces the Maximum range for a Projectile? Derive an expression for the horizontal distance a projectile travels, and determine what launch angle produces the maximum range. Assume the projectile lands at the same height it was launched from.
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Polymer Physics
Astronaut Training Astronauts undergo large accelerations while operating the spacecraft during take-off. They train for this in centrifuges such as that shown in Figure 4-22. The astronauts sit in the training capsules located at the ends of the centrifuge arms, and the entire device is rotated about a vertical axis. Figure 4-22 The Ames Research Center centrifuge. Suppose a training capsule is designed to achieve radial accelerations of 11.0g. The capsule is on the end of an arm that rotates at a constant angular speed. The radius of the horizontal circular path the capsule follows is 16.0 m. Find the period of the capsule, that is, how long it takes the capsule to complete one full trip around the circle.
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Polymer Physics
Non-uniform Circular Motion Starting from rest, an experimental mini-drone (remote-controlled aircraft) flies around a horizontal circle of radius 2.00 m and completes three revolutions in 3.00 s. The magnitude of the tangential acceleration is constant. Find the magnitude of the mini-drone’s acceleration at the end of 0.500 s.
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Polymer Physics
Bear-Proofing a Campsite When you are back-country camping, it is recommended that you suspend your foodstuffs in the trees to prevent wild animals from getting into them. This is typically accomplished by tying a line to a rock and tossing the rock over a tree limb. One then ties the line to a sealed pack that contains the food and hoists it into the tree. Suppose the tree limb is 7.00 m above ground. You plan to launch your rock at 60.08 above the horizontal. What is the minimum launch speed required and how far back from the limb should you stand? Assume you launch the rock from a height of 1.50 m above the ground.
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Polymer Physics
Using the Time-Independent kinematics Equation A projectile is launched at an angle of 60.0° above the horizontal at a speed of 15.0 m•s-1. What is the maximum height reached above the launch point?
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Polymer Physics
Projectile Motion A basketball player is 6.00 m away from the net when she shoots the ball at an angle of 30.0° above the horizontal from a height of 2.00 m. The net is at a height of 3.05 m. How fast must she shoot the ball to sink the basket?
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Polymer Physics
Flight Plan A plane is scheduled to fly from Casablanca, Morocco, to Lisbon, Portugal, 581 km [13° W of N]. A wind is blowing at 34.0 km/h [15° N of W]. When the plane’s airspeed is 560 km/h, and the pilot flies on a direct bearing to Lisbon, how long does the flight take?
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Polymer Physics
Crossing a River on a kayak A river flows from north to south. The water speed is 2.00 m/s. You are in your kayak trying to cross the river, and you keep the kayak pointing in an easterly heading that is perpendicular to the river. Your speed in still water is 4.00 m/s. Sketch the direction in which the kayak goes. What is the velocity of the kayak relative to land?
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Polymer Physics
