Concept explainers
DATA You have constructed a hair-spray-powered potato gun and want to find the muzzle speed υ0 of the potatoes, the speed they have as they leave the end of the gun barrel. You use the same amount of hair spray each time you fire the gun. And you have confirmed by repeated firings at the same height that the muzzle speed is approximately the same for each firing. You climb on a microwave relay tower (with permission, of course) to launch the potatoes horizontally from different heights above the ground. Your friend measures the height of the gun barrel above the ground and the range R of each potato. You obtain the following data:
Each of the values of h and R has some measurement error: The muzzle speed is not precisely the same each time, and the barrel isn’t precisely horizontal. So you use all of the measurements to get the best estimate of υ0. NO wind is blowing, so you decide to ignore air resistance. You use g = 9.80 m/s2 in your analysis. (a) Select a way to represent the data well as a straight line, (b) Use the slope of the best-fit line from part (a) to calculate the average value of υ0. (c) What would be the horizontal range of a potato that is fired from ground level at an angle of 30.0° above the horizontal? Use the value of υ0 that you calculated in part (b).
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
University Physics, Volume 2 - Technology Update Custom Edition for Texas A&M - College Station, 2/e
Additional Science Textbook Solutions
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Introduction to Electrodynamics
Physics: Principles with Applications
Life in the Universe (4th Edition)
Physics (5th Edition)
An Introduction to Thermal Physics
- A rugby player runs with the ball directly toward his opponent’s goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball’s velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative to the field while he passes the ball with velocity relative to himself. If has magnitude 6.0 m/s, what is the smallest angle it can have for the pass to be legal?arrow_forwardQuestion 2: #63 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 con-fined 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? 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?arrow_forwardOlympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what Initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2 .arrow_forward
- If a projectile is fired from the origin of the coordinate system with an initial velocity υ0 and in a direction making an angle α with the horizontal, calculate the time required for the projectile to cross a line passing through the origin and making an angle β < α with the horizontal.arrow_forwardA particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial velocity of vi=5.00im/s. Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s, and (d) the speed of the particle at t = 2.00 s.arrow_forwardAt t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.arrow_forward
- In the blizzard of ’88, a rancher was forced to drop hay bales from an airplane to feed her cattle. The plane flew horizontally at 160 km/hr and dropped the bales from a height of 80 m above the flat range, (a) She wanted the bales of hay to land 30 m behind the cattle so as to not hit them. Where should she push the bales out of the airplane? (b) To not hit the cattle, what is the largest time error she could make while pushing the bales out of the airplane? Ignore air resistance.arrow_forwardA stone is thrown horizontally from the highest point of a 95 m building and lands 115 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw. How long is the stone in the air in seconds? What must have been the initial horizontal component of the velocity, in meters per second? What is the vertical component of the velocity just before the stone hits the ground, in meters per second? What is the magnitude of the velocity of the stone just before it hits the ground, in meters per second?arrow_forwardin a relief operation mission involving a helicopter h distance above the ground traveling with a horizontal velocity vx. what should be the expression for the horizontal distance dx at which you release the relief package so that it will arrive to the survivors at the right place?arrow_forward
- A fireworks show is choreographed to have two shells cross paths at a height of 154 feet and explode at an apex of 191 feet under normal weather conditions. If the shells have a launch angle θ = 56° above the horizontal, determine the common launch speed v0 for the shells, the separation distance d between the launch points A and B, and the time t from the launch at which the shells explode.arrow_forwardA ball is tossed horizontally from the highest point of a 75 m building and lands 150 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw. How long is the ball in the air for, in seconds?arrow_forwardMiltiadis Tentoglou is the current Olympic gold medalist for the running long jump. In one of Miltiadis’ practices, he insanely attempts to jump five people who are laid out on the ground in single file from head to toe. Each of the five individuals are 1.7 meters in height and when Miltiadis launches off the ground his initial resultant velocity is directed 20 degrees above the horizon and the horizontal component of this resultant velocity is 10 m/s. In executing the jump, Miltiadis’ center of mass drops 0.6 meters vertically from the instant of takeoff to the instant of landing. Calculate Miltiadis’ a) initial and final vertical velocities in m/s, b) initial and final resultant velocity magnitudes in m/s, c) total time in the air in seconds and d) how far he was able to jump horizontally in meters. e) How many centimeters of clearance did Miltiadis have on both sides of the jump when jumping the five individuals (assume the clearance distance is the same on both sides of the…arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning