Almalki Aa79893 Assignment 4 Kumar 1824251 Print Out

Almalki Aa79893 Assignment4 Kumar 1824251 1this Print Out Sh

Almalki (aa79893) – assignment4 – kumar – ( This print-out should have 38 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points Aparticle moves in the xy plane with constant acceleration. At time zero, the particle is at x = 7.5 m, y = 3.5 m, and has velocity ~vo = (5.5 m/s) ı̂ + (−1.5 m/s) ̂ . The acceleration is given by ~a = (8 m/s2) ı̂+ (8.5 m/s2) ̂ . What is the x component of velocity after 2 s? Answer in units of m/s. 002 (part 2 of 3) 10.0 points What is the y component of velocity after 2 s? Answer in units of m/s. 003 (part 3 of 3) 10.0 points What is the magnitude of the displacement from the origin (x = 0 m, y = 0 m) after 2 s? Answer in units of m. 004 (part 1 of 4) 10.0 points A plane is flying horizontally with speed 169 m/s at a height 4160 m above the ground, when a package is dropped from the plane. The acceleration of gravity is 9.8 m/s2 . Neglecting air resistance, when the package hits the ground, the plane will be 1. behind the package, 2. ahead of the package, or 3. directly above the package. 005 (part 2 of 4) 10.0 points What is the horizontal distance from the release point to the impact point? Answer in units of m. 006 (part 3 of 4) 10.0 points A second package is thrown downward from the plane with a vertical speed v1 = 52 m/s. What is the magnitude of the total velocity of the package at the moment it is thrown as seen by an observer on the ground? Answer in units of m/s. 007 (part 4 of 4) 10.0 points What horizontal distance is traveled by this package? Answer in units of m. 008 10.0 points Assume: A 78 g basketball is launched at an angle of 42.1° and a distance of 14.9 m from the basketball goal. The ball is released at the same height (ten feet) as the basketball goal’s height. A basketball player tries to make a long jump-shot as described above. The acceleration of gravity is 9.8 m/s2 . What speed must the player give the ball? Answer in units of m/s. 009 10.0 points A 0.33 kg rock is projected from the edge of the top of a building with an initial velocity of 7.13 m/s at an angle 38° above the horizontal. Due to gravity, the rock strikes the ground at a horizontal distance of 11.7 m from the base of the building. How tall is the building? Assume the ground is level and that the side of the building is vertical. The acceleration of gravity is 9.8 m/s2 . Answer in units of m. 010 10.0 points A boat moves through the water of a river at 6.62 m/s relative to the water, regardless of the boat’s direction. If the current is flowing at 5.75 m/s, how long does it take the boat to complete a trip consisting of a 235 m displacement downstream followed by a 149 m displacement upstream? Answer in units of s. 011 (part 1 of 3) 10.0 points Two cars approach each other; both cars are moving westward, one at 83 km/h, the other at 63 km/h. What is the magnitude of the velocity of the first car relative to the second car? Answer in units of km/h. 012 (part 2 of 3) 10.0 points What is the direction of the resultant velocity? 1. Eastward 2. Unable to determine. 3. Westward 013 (part 3 of 3) 10.0 points After they pass, how will their relative velocity change? 1. Unable to determine 2. Greater than before 3. Less than before 4. No change 014 (part 1 of 2) 10.0 points A camel sets out to cross the desert, which is 35.5 km wide in the north-south direction. The camel walks at the uniform speed 4.53 km/hr along a straight line in the direction 42.2° north of East (only the camel knows why he chose that particular direction). How long will it take the camel to cross the desert? Answer in units of hr. 015 (part 2 of 2) 10.0 points Calculate the camel’s eastward displacement while he crosses the desert. Answer in units of km. 016 (part 1 of 2) 10.0 points A truck travels beneath an airplane that is moving 100 km/h at an angle of 55° to the ground. How fast must the truck travel to stay beneath the airplane? Answer in units of km/h. 017 (part 2 of 2) 10.0 points What is the magnitude of the vertical component of the velocity of the plane? Answer in units of km/h. 018 (part 1 of 2) 10.0 points A superhero flies 310 m from the top of a tall building at an angle of 30° below the horizontal. What is the horizontal component of the superhero’s displacement? Draw the vectors to scale on a graph to determine the answer. Answer in units of m. Your answer must be within ± 5.0%. 019 (part 2 of 2) 10.0 points What is the vertical component of the superhero’s displacement? Answer in units of m. Your answer must be within ± 5.0%. 020 (part 1 of 4) 10.0 points A shopper pushing a cart through a store moves 30.0 m south down one aisle, then makes a 90° turn and moves 15.0 m. He then makes another 90° turn and moves 19.0 m. What is the magnitude of the smallest possible displacement the shopper could have? You are not given the direction moved after any of the 90° turns, so there could be more than one answer. Answer in units of m. 021 (part 2 of 4) 10.0 points At how many degrees from due south is this displacement? Answer in units of °. 022 (part 3 of 4) 10.0 points What is the magnitude of the largest possible displacement the shopper could have? Answer in units of m. 023 (part 4 of 4) 10.0 points At how many degrees from due south is this displacement? Answer in units of °. 024 10.0 points The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction 64.0° north of west with a speed of 49.7 km/h. Exactly 3.11 hours later, the course of the hurricane shifts due north, and its speed slows to 28.6 km/h, as shown. How far from Grand Bahama is the hurricane 4.54 h after it passes over the island? Answer in units of km. 025 10.0 points A person walks 35 m East and then walks 36 m at an angle 40° North of East. What is the magnitude of the total displacement? Answer in units of m. 026 (part 1 of 2) 10.0 points Instructions for finding a buried treasure include the following: Go 527.9 paces at 298°, turn to 115° and walk 251 paces, then travel 370 paces at 282°. Find the magnitude of the resultant displacement from the starting point. Answer in units of paces. 027 (part 2 of 2) 10.0 points What is the direction of the resultant displacement? Use counterclockwise from due East as the positive angular direction, between the limits of −180° and +180°. Answer in units of °. 028 (part 1 of 2) 10.0 points Consider four vectors ~F1, ~F2, ~F3, and ~F4 with magnitudes F1 = 53 N, F2 = 21 N, F3 = 24 N, and F4 = 56 N, θ1 = 120°, θ2 = −140°, θ3 = 39°, and θ4 = −51°, measured from the positive x axis with counterclockwise positive. What is the magnitude of the resultant vector ~F = ~F1 + ~F2 + ~F3 + ~F4? Answer in units of N. 029 (part 2 of 2) 10.0 points What is the direction of this resultant vector ~F, within the limits of −180° and 180° as measured from the positive x axis with counterclockwise positive? Answer in units of °. 030 (part 1 of 6) 10.0 points Find the magnitude and direction of the vector sum ~R1 where ~R1 = ~A + ~B. The vector ~A = 10.8 m at an angle 180° from the positive horizontal axis, and ~B = 19.2 m at an angle 44° from the positive horizontal axis. Answer in units of m. 031 (part 2 of 6) 10.0 points At what angle (between −180° and 180° with 0° the positive x axis and counterclockwise positive) is the vector sum? Answer in units of °. 032 (part 3 of 6) 10.0 points What is the magnitude of the vector difference ~A− ~B? Answer in units of m. 033 (part 4 of 6) 10.0 points At what angle (between −180° and 180° with 0° the positive x axis) is the direction of this resulting vector? Answer in units of °. 034 (part 5 of 6) 10.0 points What is the magnitude of the vector difference ~B − ~A? Answer in units of m. 035 (part 6 of 6) 10.0 points At what angle (between −180° and 180° with 0° the positive x axis) is the direction of this resulting vector? Answer in units of °. 036 (part 1 of 3) 10.0 points Neglect: Air friction. Your teacher tosses a basketball. The ball gets through the hoop (lucky shot). b = 2.484 m, h = 3.048 m, v = 18 m/s, and the angle = 49°. How long does it take the ball to reach its maximum height? Answer in units of s. 037 (part 2 of 3) 10.0 points How long does it take the ball to reach the hoop? Answer in units of s. 038 (part 3 of 3) 10.0 points What is the horizontal length l of the shot? Answer in units of m.

Paper For Above instruction

This comprehensive physics analysis explores a wide array of classical mechanics problems, emphasizing the fundamental principles of kinematics, dynamics, and projectile motion. The questions address key concepts such as constant acceleration, relative velocity, projectile trajectory, and forces, providing a detailed understanding of motion in various contexts. The solutions underscore the application of equations of motion and vector analysis to real-world scenarios, facilitating the development of problem-solving skills essential for physics students.

Introduction

Physics, the fundamental science of matter and energy, critically examines the laws governing motion. The examined problems encapsulate typical scenarios faced in physics, from particles moving under constant acceleration to complex vector compositions. These illustrations serve to reinforce core concepts such as Newtonian mechanics, relative motion, and the principles of projectile motion, fostering deep comprehension of the interactions involved in dynamic systems.

Particle Motion with Constant Acceleration

The initial problems involve a particle moving in the xy-plane with a known initial velocity and constant acceleration. The x and y components of velocity after a specific time are derived from the equations:

v_x = v_{0x} + a_x t, and v_y = v_{0y} + a_y t,

where v_{0x} and v_{0y} are initial velocities, a_x and a_y are accelerations, and t is time.

Given the initial velocities of 5.5 m/s in x and -1.5 m/s in y, with accelerations of 8 m/s² and 8.5 m/s² respectively, after 2 seconds, the velocity components are calculated as follows:

• x component: v_x = 5.5 + (8)(2) = 5.5 + 16 = 21.5 m/s
• y component: v_y = -1.5 + (8.5)(2) = -1.5 + 17 = 15.5 m/s

The magnitude of displacement from the origin after 2 seconds considers both the x and y displacements, obtained via:

x = v_{0x} t + (1/2) a_x t^2, y = v_{0y} t + (1/2) a_y t^2,

leading to the overall displacement vector and its magnitude calculated through Pythagoras.

Projectile Motion and Impact Analysis

The problem involving a package dropped from an aircraft at 4160 meters with a horizontal speed of 169 m/s examines the projectile trajectory neglecting air resistance. The key is to determine the impact point considering the time of fall using the equation:

t = sqrt(2h / g),

and then computing the horizontal distance as:

d = v_{horizontal} * t.

Similarly, when a package is thrown downward with an initial vertical velocity, the total velocity at impact combines horizontal and vertical components, using vector addition:

v_total = sqrt(v_x^2 + v_y^2),

plus calculation of horizontal displacement considering initial vertical velocity and time of flight.

Projectile Velocity and Distance Calculations

For launching projectiles such as a basketball or determining the needed initial speed for a successful shot, the equations of motion provide the necessary relations:

Range R = (v^2 sin 2θ) / g,

which helps in ascertaining the initial velocity given a range, launch angle, and height. Solving quadratic equations for vertical motion further determines the height and time of flight.

The problem involving the projection of a rock from a building applies kinematic equations to find the building’s height, using the horizontal and vertical displacement equations in conjunction with initial velocity and angle.

Relative Motion in Fluids and Vehicles

In studies of relative velocities, such as a boat moving across a river or cars approaching each other, vector addition and subtraction are fundamental. Calculations of time for downstream and upstream trips use the effective velocities:

v_{effective} = v_{boat} ± v_{current}.

Similarly, the relative velocity between two cars moving westward involves vector subtraction, and the resultant speed is obtained via the Pythagorean theorem for vectors pointing in the same or opposite directions.

Navigation, Travel, and Displacement

The camel crossing the desert and the hurricane’s path are classical examples of navigation and vector addition. The displacement calculations involve resolving the movement into components using trigonometry, then calculating the resultant magnitude and direction from these components.

The hurricane's movement illustrates vector addition with changing speed and direction, emphasizing the importance of understanding vector components and their resultant for real-world weather tracking.

Vector Addition and Subtraction in Multiple Dimensions

The problems involving vectors ~F1, ~F2, ~F3, and ~F4 or summing vectors ~A and ~B exemplify the importance of component-wise addition for obtaining magnitude and direction. Applying the law of cosines and sines, combined with transformation into component form, enables precise calculation of resultant vectors.

Final Remarks and Application of Physics Principles

These problems encapsulate the essence of classical mechanics, highlighting the importance of understanding and applying kinematic equations, vector principles, and trigonometry in analyzing physical systems. Mastery of these concepts enhances problem-solving skills relevant across physics disciplines and real-world engineering applications.

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