College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Textbook Question
Chapter 3, Problem 31PE
Verify the ranges for the projectiles in Figure 3.41(a) for
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In measuring values of distance and height, we can assume that measurements can be made with a measurement error of 0.05 m. Assume a projectile is launched horizontally with a height of 3 m, with a resulting range of 21.1 m. Using Min/Max and the equations of motion for a projectile, determine the time of flight of the projectile with most probable error.
I am working on finding the inital velocity of a class II projectile and am having trouble determining the right amount of sig figs.
The taken measurements of the initial position of x goes to 4 sig figs, as well as the final position for y.
With that being said, I am trying to find the initial velocity of x and y separately through trionometry. For example, if I have an equation for the initial velocity of x with an angle of 40, then
Vox=Vocos40
My question is, since the measured value for my angle is two significant figures, is my answer Vox=.76Vo also in two sig figs because it goes by the two significant figures from my measured angle, or should I go to four significant figures to match my measured values for x and y?
A mortar shell is to be fired from level ground so as to clear a flat topped building
of height h and width a. The mortar gun can be placed anywhere on the ground and
can have any angle of elevation. What is the least projection speed that will allow
the shell to clear the building? [Hint How is the reqired minimum projection speed
changed if the mortar is raised to rooftop level?]
=
For the special case in which h a, find the optimum position for the mortar
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Chapter 3 Solutions
College Physics
Ch. 3 - Which of the following is a vector: a person's...Ch. 3 - Give a specific example of a vector, stating its...Ch. 3 - What do vectors and scalars have in common? How do...Ch. 3 - Two calipers in a national park hike from their...Ch. 3 - If an airplane plot is told to fly 123 km in a...Ch. 3 - Suppose you take two steps A and B (that is, two...Ch. 3 - Explain why it is not possible to add a scalar to...Ch. 3 - If you take two steps of different sizes, can you...Ch. 3 - Suppose you add two vectors A and B. What relative...Ch. 3 - Give an example of a nonzero vector that has a...
Ch. 3 - Explain why a vector cannot have a component...Ch. 3 - If the vectors A and B are perpendicular, what is...Ch. 3 - Answer the following questions for projectile...Ch. 3 - Answer the following questions for projectile...Ch. 3 - For a fixed initial speed, the range of a...Ch. 3 - During a lecture demonstration, a professor places...Ch. 3 - What frame or frames of reference do you...Ch. 3 - A basketball player dribbling clown the court...Ch. 3 - If someone riding in the back of a pickup truck...Ch. 3 - The hat of a jogger running at constant velocity...Ch. 3 - A clod of dirt falls from the bed of a moving...Ch. 3 - Find the following for path A in Figure 3.54: (a)...Ch. 3 - Find the following for path B in Figure 3.54: (a)...Ch. 3 - Find the north and east components of the...Ch. 3 - Suppose you walk 18.0 m straight west and then...Ch. 3 - Suppose you first walk 12.0 m in a direction 20°...Ch. 3 - Repeat the problem above, but reverse the order of...Ch. 3 - (a) Repeat the problem two problems prior, but for...Ch. 3 - Show that the order of addition of three vectors...Ch. 3 - Show that the sum of the vectors discussed in...Ch. 3 - Find the magnitudes of velocity vAand vBin figure...Ch. 3 - Find the components of vtot along the x- and...Ch. 3 - Find the components of vtot along a set of...Ch. 3 - Find the following for path C in Figure 3.58: (a)...Ch. 3 - Find the following for path D in Figure 3.58: (a)...Ch. 3 - Find the north and east components of the...Ch. 3 - Solve the following problem using analytical...Ch. 3 - Repeat Exercise 3.16 using analytical techniques,...Ch. 3 - You drive 7.50 km in a straight line in a...Ch. 3 - Do Exercise 3.16 again using analytical techniques...Ch. 3 - A new landowner has a triangular piece of flat...Ch. 3 - You fly 32.0 km in a straight line in still air in...Ch. 3 - A farmer wants to fence off his four-sided plot of...Ch. 3 - In an attempt to escape his island, Gilligan...Ch. 3 - Suppose a pilot flies 40.0 km in a direction 60°...Ch. 3 - A projectile is launched at ground level with an...Ch. 3 - A ball is kicked with an initial velocity of 16...Ch. 3 - A ball is thrown horizontally from the top of a...Ch. 3 - (a) A daredevil is attempting to jump his...Ch. 3 - An archer shoots an arrow at a 75.0 m distant...Ch. 3 - A rugby player passes the ball 7.00 m across the...Ch. 3 - Verify the ranges for the projectiles in Figure...Ch. 3 - Verity the ranges shown for the projectiles in...Ch. 3 - The cannon on a battleship can fire a shell a...Ch. 3 - An arrow is shot from a height of 1.5 m toward a...Ch. 3 - In the standing broad jump, one squats and then...Ch. 3 - The world long jump record is 8.95 m (Mike Powell,...Ch. 3 - Serving at a speed of 170 km/h, a tennis player...Ch. 3 - A football quarterback is moving straight backward...Ch. 3 - Gun sights are adjusted to aim high to compensate...Ch. 3 - An eagle is flying horizontally at a speed of 3.00...Ch. 3 - An owl is carrying a mouse to the chicks in its...Ch. 3 - Suppose a soccer player kicks the ball from a...Ch. 3 - Can a goalkeeper at her/ his goal kick a soccer...Ch. 3 - The free throw line in basketball is 4.57 m (15...Ch. 3 - In 2007, Michael Carter (U.S.) set a world record...Ch. 3 - A basketball player is running at 5.00 m/s...Ch. 3 - A football player punts the ball at a 45.0° angle....Ch. 3 - Prove that the trajectory of a projectile is...Ch. 3 - Derive R=v02sin20g for the range of a projectile...Ch. 3 - Unreasonable Results (a) Find the maximum range of...Ch. 3 - Construct Your Own Problem Consider a ball tossed...Ch. 3 - Bryan Allen pedaled a human-powered aircraft...Ch. 3 - A seagull flies at a velocity of 9.00 m/s straight...Ch. 3 - Near the end of a marathon race, the first two...Ch. 3 - Verity that the coin dropped by the airline...Ch. 3 - A football quarterback is moving straight backward...Ch. 3 - A ship sets sail from Rotterdam, The Netherlands,...Ch. 3 - (a) A jet airplane flying from Darwin, Australia,...Ch. 3 - (a) In what direction would the ship in Exercise...Ch. 3 - (a) Another airplane is flying in a jet stream...Ch. 3 - A sandal is dropped from the top of a 15.0-m-high...Ch. 3 - The velocity of the wind relative to the water is...Ch. 3 - The great astronomer Edwin Hubble discovered that...Ch. 3 - (a) Use the distance and velocity data in Figure...Ch. 3 - An athlete crosses a 25-m-wide river by swimming...Ch. 3 - A ship sailing in the Gulf Stream is heading 25.0°...Ch. 3 - An ice hockey player is moving at 8.00 m/s when he...Ch. 3 - Unreasonable Results Suppose you wish to shoot...Ch. 3 - Unreasonable Results A commercial airplane has an...Ch. 3 - Construct Your Own Problem Consider an airplane...
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- A projectile is fired with an initial speed of 36.5 m/sm/s at an angle of 41.1 ∘∘ above the horizontal on a long flat firing range. Determine the speed of the projectile 1.90 ss after firing. Express your answer using three significant figures and include the appropriate units.arrow_forwardA ground-to-ground projectile is shot with an initial velocity of 18 m/sat angle 54 degrees, measured from the horizontal. Neglecting air-resistance, what is the range of the projectile (the maximum horizontal distance in meter)?arrow_forwardA radar station sends a signal to a ship which is located a distance 13.8 kilometers from the station at bearing 136° clockwise from the north. At the same moment, a helicopter is at a horizontal range of 19.6 kilometers, at bearing 146° clockwise from the north, with an elevation of 2.56 kilometers. Let east be the î direction, north be the ĵ direction, and up be the direction. a) What If? The ship begins to sink at a rate of 5.50 m/s. Write the position vector (in km) of the ship relative to the helicopter as a function of time as the ship sinks. Assume that the helicopter remains hovering at its initial position and that the sinking rate remains the same even after the ship sinks under the surface.arrow_forward
- A projectile is fired with an initial speed of 36.5 m/sm/s at an angle of 41.1 ∘∘ above the horizontal on a long flat firing range. Determine the total horizontal distance covered (that is, the range). Express your answer using three significant figures and include the appropriate units.arrow_forwardAt t=0, a particle is projected with a speed Vo at angle theta from a cliff point H=100m from ground level as shown. It is seen at time t=2s, having a velocity v(t2)=8i ‐ 11j m/s according to the coordinate system shown. You must use this coordinate system and origin O. a)Find V o, and theta o. b) If the cliff height is H=100m, write a numerical expression for (t2) in unit vector notation. You must use the origin O and then draw r (t2) on the diagram. c)Find R, the horizontal distance the object has traveled when it reaches its highest point.arrow_forwardA jet plane is observed 400ft above the ground and is flying 180 mph to the west. A man jumps out of the plane creating a projectile motion and recorded that he is descending at a constant velocity of 6 ft/s after he reached an observable distance from the ground. If the man is to reach the ground 37 seconds after his immediate jump off the plane, determine the range of the initial position of the plane to the target landing of the man in the ground. a) 601.29 ft b) 1111.31 ft c) 28.38 ft d) 1000.12 ftarrow_forward
- 2.34 At what true anomaly does the speed on a parabolic trajectory equal a times the speed at the periapsis, where a < 1?arrow_forwardA mortar gun, with a maximum range of 20 m on level ground, is placed on the edge of a vertical cliff of height 10 m overlooking a horizontal plane, as illustrated in the following figure. 20 m (a) Consider the sub-problem of the mortar gun on level ground with maximum range of 20 m. Show that the flight time for the projectile on level ground is V2 vo Hint: The angle required to obtain maximum range is 0 = T/4.arrow_forwardA projectile is fired from a platform that is moving horizontally with velocity V = (V, 0, 0). The initial velocity of the projectile relative to the platform is u = (U₁, U₂, 0). Show that the range on a horizontal plane through the platform is u² R(6) = sin 2Vu sin 20 +- sin 0, (1) 9 9 where u = √√√u?+ u² and 0 is the angle of projection (0 ≤ 0 ≤ ). Determine the value of that makes R a maximum, and calculate Rmax in terms of u, V and g.arrow_forward
- Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in figure. The speed of A is 100/3 m/s. At time t = Os , an observer in y – axis finds B at a distance of 500 m .This observer sees B moving with a constant velocity perpendicular to the line of motion of A If at t = to , A just escapes being hit by B , to in seconds is, B -30°arrow_forwardA projectile is shot from the edge of a cliff 115 m above ground level with an initial speed of vo = 54 m/s at an angle of 35.0° with the horizontal, as shown in the figure (Figure 1). Figure 35.0 h = 115m 1 of 1 Part E At the instant just before the projectile hits point P, find the angle made by the velocity vector with the horizontal. Express your answer to three significant figures and include the appropriate units. 0= Part F Submit Request Answer μA + Max = Value MacBook Air μA Value P Pearson → Find the maximum height above the cliff top reached by the projectile. Express your answer to three significant figures and include the appropriate units. Units a ? Units Review I Constants below the horizon ? Copyright © 2022 Pearson Education Inc. All rights reserved. | Terms of Use | Privacy Policy | Permissions Contact Usarrow_forwardProblem 3.3 Prove that the components of a vector with respect to a given basis are unique.arrow_forward
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