College Physics: A Strategic Approach (4th Edition)
4th Edition
ISBN: 9780134609034
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Chapter 3, Problem 63GP
In 1780, in what is now referred to as “Brady’s Leap,” Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio’s Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. Tall tale, or possible?
Figure P3.63
a. What is the minimum speed with which he’d need to run off the edge of the cliff to make it safely to the far side of the river?
b. The world-record time for the 100 m dash is approximately 10 s. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady’s leap?
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In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running over the edge of the cliff above Ohio's Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. (Figure 1)
A. Representing the horizontal distance jumped as L and the vertical drop as h , as shown in the figure, derive an expression for the minimum speed v he would need to make his leap if he ran straight off the cliff.
Express your answer in terms of the given quantities and appropriate constants.
B. Evaluate your expression for a 22 ft jump with a 20 ft drop to the other side.
C. Is it reasonable that a person could make this leap? Use the fact that the world record for the 100 m dash is approximately 10 s to estimate the maximum speed such a runner would have. (Yes or no answer)
An engineer designs a roller coaster so that a car travels horizontally for 192 ft,then climbs 137 ft at an angle of 33.0° above the horizontal. It then moves 137 ft at an angle of 48.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)
An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 147 ft at an angle of 33.0° above the horizontal. It then moves 147 ft at an angle of 42.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)
magnitude ____ft
direction _____° counterclockwise from the +x-axis
Chapter 3 Solutions
College Physics: A Strategic Approach (4th Edition)
Ch. 3 - a. Can a vector have nonzero magnitude if a...Ch. 3 - Prob. 2CQCh. 3 - Suppose two vectors have unequal magnitudes. Can...Ch. 3 - Prob. 4CQCh. 3 - For a projectile, which of the following...Ch. 3 - A baseball player throws a ball at a 40 angle to...Ch. 3 - An athlete performing the long jump tries to...Ch. 3 - If you kick a football, at what angle to the...Ch. 3 - Prob. 9CQCh. 3 - Prob. 10CQ
Ch. 3 - If you go to a ski area, youll likely find that...Ch. 3 - In an amusement-park ride, cars rolling along at...Ch. 3 - There are competitions in which pilots fly small...Ch. 3 - Prob. 14CQCh. 3 - You are cycling around a circular track at a...Ch. 3 - An airplane has been directed to fly in a...Ch. 3 - When you go around a corner in your car, your car...Ch. 3 - A person trying to throw a ball as far as possible...Ch. 3 - Prob. 19CQCh. 3 - Prob. 20MCQCh. 3 - Prob. 21MCQCh. 3 - The gas pedal in a car is sometimes referred to as...Ch. 3 - A car travels at constant speed along the curved...Ch. 3 - Prob. 24MCQCh. 3 - Prob. 25MCQCh. 3 - Prob. 26MCQCh. 3 - Prob. 27MCQCh. 3 - A football is kicked at an angle of 30 with a...Ch. 3 - A football is kicked at an angle of 30 with a...Ch. 3 - Prob. 30MCQCh. 3 - Formula One race cars are capable of remarkable...Ch. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - A position vector with magnitude 10 m points to...Ch. 3 - A velocity vector 40 above the positive x-axis has...Ch. 3 - A cannon tilted upward at 30 fires a cannonball...Ch. 3 - Prob. 8PCh. 3 - Draw each of the following vectors, then find its...Ch. 3 - Draw each of the following vectors, then find its...Ch. 3 - Each of the following vectors is given in terms of...Ch. 3 - Each of the following vectors is given in terms of...Ch. 3 - A wildlife researcher is tracking a flock of...Ch. 3 - Jack and Jill ran up the hill at 3.0 m/s. The...Ch. 3 - Josh is climbing up a steep 34 slope, moving at a...Ch. 3 - You begin sliding down a 15 ski slope. Ignoring...Ch. 3 - A car traveling at 30 m/s runs out of gas while...Ch. 3 - In the Soapbox Derby, young participants build...Ch. 3 - A piano has been pushed to the top of the ramp at...Ch. 3 - Prob. 20PCh. 3 - A car goes around a corner in a circular arc at...Ch. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - A ball is thrown horizontally from a 20-m-high...Ch. 3 - A ball with a horizontal speed of 1.25 m/s rolls...Ch. 3 - A pipe discharges storm water into a creek. Water...Ch. 3 - A pipe discharges storm water into a creek. Water...Ch. 3 - Prob. 31PCh. 3 - A rifle is aimed horizontally at a target 50 m...Ch. 3 - A gray kangaroo can bound across a flat stretch of...Ch. 3 - On the Apollo 14 mission to the moon, astronaut...Ch. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Racing greyhounds are capable of rounding corners...Ch. 3 - To withstand g-forces of up to 10 gs, caused by...Ch. 3 - Prob. 39PCh. 3 - In a roundabout (or traffic circle), cars go...Ch. 3 - A particle rotates in a circle with centripetal...Ch. 3 - Entrance and exit ramps for freeways are often...Ch. 3 - A peregrine falcon in a tight, circular turn can...Ch. 3 - An airplane cruises at 880 km/h relative to the...Ch. 3 - Anita is running to the right at 5 m/s, as shown...Ch. 3 - Anita is running to the right at 5 m/s, as shown...Ch. 3 - Two children who are bored while waiting for their...Ch. 3 - A boat takes 3.0 h to travel 30 km down a river,...Ch. 3 - A particle rotates in a circle with centripetal...Ch. 3 - Suppose D=AB where vector A has components Ax = 5,...Ch. 3 - Suppose E = 2A+3B where vector A has components Ax...Ch. 3 - For the three vectors shown in Figure P3.47, the...Ch. 3 - Prob. 54GPCh. 3 - Prob. 55GPCh. 3 - A pilot in a small plane encounters shifting...Ch. 3 - Prob. 57GPCh. 3 - Prob. 58GPCh. 3 - A skier gliding across the snow at 3.0 m/s...Ch. 3 - Prob. 60GPCh. 3 - A physics student on Planet Exidor throws a ball,...Ch. 3 - Prob. 62GPCh. 3 - In 1780, in what is now referred to as Bradys...Ch. 3 - The longest recorded pass in an NFL game traveled...Ch. 3 - A spring-loaded gun, fired vertically, shoots a...Ch. 3 - Small-plane pilots regularly compete in message...Ch. 3 - Prob. 67GPCh. 3 - Trained dolphins are capable of a vertical leap of...Ch. 3 - A tennis player hits a ball 2.0 m above the...Ch. 3 - The shot put is a track-and-field event in which...Ch. 3 - Water at the top of Horseshoe Falls (part of...Ch. 3 - A supply plane needs to drop a package of food to...Ch. 3 - Prob. 73GPCh. 3 - Ships A and B leave port together. For the next...Ch. 3 - A flock of ducks is trying to migrate south for...Ch. 3 - A kayaker needs to paddle north across a...Ch. 3 - A plane has an airspeed of 200 mph. The pilot...Ch. 3 - The Gulf Stream off the east coast of the United...Ch. 3 - A ball thrown horizontally at 25 m/s travels a...Ch. 3 - A sports car is advertised as capable of reaching...Ch. 3 - A Ford Mustang can accelerate from 0 to 60 mph in...Ch. 3 - The Screaming Swing is a carnival ride that isnot...Ch. 3 - On an otherwise straight stretch of road near...Ch. 3 - Prob. 84MSPPCh. 3 - Prob. 85MSPPCh. 3 - Prob. 86MSPPCh. 3 - Prob. 87MSPPCh. 3 - Prob. 88MSPP
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