An arrow is fired with an initial velocity v0 at an angle θ0 above horizontal. Assume the arrow moves without air resistance. Use the Cartesian coordinate system provided, with the origin at the arrow's initial position. At some later time, t, the arrow makes an angle of θθ with respect to the horizontal. Enter an expression for the time, t.

An arrow is fired with an initial velocity v0 at an angle θ0 above horizontal. Assume the arrow moves without air resistance. Use the Cartesian coordinate system provided, with the origin at the arrow's initial position. At some later time, t, the arrow makes an angle of θθ with respect to the horizontal. Enter an expression for the time, t.

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Description: An arrow is fired with an initial velocity v0 at an angle θ0 above horizontal. Assume the arrow moves without air resistance. Use the Cartesian coordinate system provided, with the origin at the arrow's initial position.At some later time, t, the arr

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 16P: A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at...

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An arrow is fired with an initial velocity v0 at an angle θ0 above horizontal. Assume the arrow moves without air resistance. Use the Cartesian coordinate system provided, with the origin at the arrow's initial position. At some later time, t, the arrow makes an angle of θ with respect to the horizontal. Enter an expression for the time, t.
An arrow is fired with an initial velocity v0 at an angle θ0 above horizontal. Assume the arrow moves without air resistance. Use a Cartesian coordinate system with the origin at the arrow's initial position to analyze the arrow's motion. Some time later the arrow makes an angle of θ = 15 degrees with respect to the horizontal. Write an expression for the time, t, that passes between when the arrow was fired and this later point. t = ?
An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.
Consider the following scenario. A pilot is steering a plane in the direction N 45° W at an air-speed (speed still in air) of 150 mi/h. A wind is blowing in the direction S 30° E at a speed of 34 mi/h. Set up the coordinate axes so that north is the positive y-direction and west is the negative x-direction. With respect to the still air, write a vector that represents the velocity of the plane and a vector that represents the velocity of the wind. plane Give a velocity vector of the plane relative to ground. (Round your values to three decimal places.) V=Vane + wind" Find vl. (Round your answer to one decimal place.) |v| Find the true course and the ground speed (in mi/h) of the plane. (Round your answers to one decimal place.) true course N x w ground speed x mi/h
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As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 63.0° north of west with a speed of 40.2 km/h. (Let i represent east and j represent north.) (a) What is the unit-vector expression for the velocity of the hurricane? km/h i+ km/hi It maintains this velocity for 3.50 h, at which time the course of the hurricane suddenly shifts due north, and its speed slows to a constant 25.2 km/h. This new velocity is maintained for 1.50 h. (b) What is the unit-vector expression for the new velocity of the hurricane? km/h j km/h i+ (c) What is the unit-vector expression for the displacement of the hurricane during the first 3.50 h? km i+ km j (d) What is the unit-vector expression for the displacement of the hurricane during the latter 1.50 h? km i+ km j (e) How far from Grand Bahama is the eye 5.00 h after it passes over the island? km
A cannon ball is fired with an initial speed of 123 m/s at angle of 60 degrees from the horizontal. Express the initial velocity as a linear combination of its unit vector components. Vo = ( m/s) î + ( /s) ? m At the maximum height, the speed of the cannon ball is v = m/s and the magnitude of its acceleration is a = m/s?. The time needed to reach maximum height ist= S. The maximum height reached by the cannon ball is H = m.
While competing in the long jump, a person leaps over a smooth horizontal sand surface. She lands on the surface with speed vf = 7.75 m/s at an angle = 33° below horizontal. Assume that the person moves without air resistance. Use a Cartesian coordinate system with the origin at her final position. The positive x-axis is directed from her initial to her final position, and the positive y-axis is directed vertically upwards. Part (a) Enter an expression for the jumper's initial velocity vector in terms of vf, 0, g, and the unit vectors i and j. Vo = Vf cos(0) i+vf sin(0) j✔ Correct! Part (b) Calculate the maximum height, in meters, that the jumper reaches above ground level. ✓ Correct! hmax=0.908 33% Part (c) What x position, in meters, did the jumper begin her long jump? xo =
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A cannon ball is fired with an initial speed of 123 m/s at angle of 60 degrees from the horizontal. Express the initial velocity as a linear combination of its unit vector components. Vo = ( m/s) î + ( m/s) Î At the maximum height, the speed of the cannon ball is v = m/s and the magnitude of its acceleration is a = m/s2. The time needed to reach maximum height is t = S. The maximum height reached by the cannon ball is H = m.
Consider a projectile being launched with an initial speed of 49.5 m/s at a variety of initial angles. Refer to the figure. Part (a) What is the range, in meters, of the projectile if it is launched at an angle of θ1 = 70.6°? b. What is the range, in meters, of the projectile if it is launched at an angle of θ2 = 38°? c. What is the range, in meters, of the projectile if it is launched at an angle of θ3 = 90 − 70.6°, the complement of θ1?