On a separate part of your paper, copy the velocity vectors
1. Is the angIe
Consider how
What value or range of values is possible for this angle for an object that is speeding up? Explain.
What happens to the magnitude of
2. Describe how you would determine the acceleration of the object at point E.
Consider the direction of the acceleration at point E. Is the angle between the acceleration vector and the velocity vector (placed “tail-to-tail”) greater than, less than, or equal to
Learn your wayIncludes step-by-step video
Chapter 1 Solutions
Tutorials in Introductory Physics
Additional Science Textbook Solutions
Physics: Principles with Applications
Essential University Physics (3rd Edition)
The Cosmic Perspective
The Cosmic Perspective (8th Edition)
Glencoe Physical Science 2012 Student Edition (Glencoe Science) (McGraw-Hill Education)
- Consider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a velocity v = (β, αz, −αy), where α and β are positive constants. (a) What are the physical dimensions of α and β? (b) Find the general form of r(t), the position of the particle, as a function of time t, assuming the initial position of the particle is r0 = (0, 2, 0) (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot). (c) Show that the speed of the particle is constant, but the acceleration vector a(t) is nonzero. Justify. Assuming the particle has a constant mass m, use Newton’s second law to show that the force acting on the particle is (as a function of the position r = (x, y, z)) F(x, y, z) = mα2(0, −y, −z).arrow_forwardPoint A moves uniformly with velocity v so that the vector v is continually “aimed” at point B which in its turn moves rectilinearly and uniformly with velocity u At the initial moment of time v perpendicular to u and the points are separated by a distance L. How soon will the points converge?arrow_forwardHello, Can someone please show how to solve parts d and e please? Thank youarrow_forward
- Can you solve this and show steps? Also, what would be the direction of vector A x B be in the x-direction? Positive z or negative z?arrow_forwardAssume that, at the initial instant to = 0, a particle is thrown with initial speed vo and with an initial angle θo, with respect to a direction parallel to the Earth's surface. In this way, in order to carry out an analytical study of its motion in a simpler way, consider a coordinate system xoy, with its origin at the particle's launch position, and with its positive x axis oriented in the direction of the horizontal motion of the particle and with its positive y-axis oriented vertically upward. In this sense, illustrate (make the force diagrams) the projectile launch, highlighting its main characteristics, and describe algebraically what is asked:arrow_forwardIf f is a scalar function and v = [v1, v2, v3] is a vector field. Show that div(fv)=f divv+v·∇farrow_forward
- Can you answer problem 1 part b?arrow_forwardDerive expressions for the velocity (~v) and acceleration (~a) vectors in spherical coordinates.That is, transform ~v and ~a from the Cartesian system of (x, y, z) to (r, θ, φ).arrow_forwardSuppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle θ above the horizontal at which it is thrown. Use the accompanying table and the equations below to estimate the partial derivatives. fx(x0,y0)= limΔx→0f(x0+Δx,y0)-f(x0,y0)Δx; fy(x0,y0) =limΔy→0f(x0,y0+Δy)-f(x0,y0)Δy Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer.(a) Estimate the partial derivative of r with respect to v when v=80ft/s and θ=45∘.arrow_forward
- Answer the following: On what plane is the vector <1,0,0> located? What is the axis of <1,0,0>? The vector <1,2,3> is a unit vector, true or false? A vector is always _____ to its unit vector representationarrow_forwardFor any arbitrary vectors u, v and w, prove thatarrow_forwardA particle is moving on top of a 2-dimensional. plane with its coordinates given in cartesian system as x(t) =a sin ωt, y(t) = a cos ωt. Express the motion of the particle in terms of polar coordinates (ρ, φ). What is the minimum number ofgeneralised coordinates required to describe. its motion? Draw the. trajectory of the particle.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning