# hw1 - Physics 318 Problem Set 1 Due Wednesday 1 A particle...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 318: Problem Set 1 Due Wednesday, Jan 30, 2008 1. A particle is projected vertically upward in a constant gravitational field with an initial velocity v . Show that if there is a retarding force proportional to the square of the instantaneous velocity, then the velocity of the particle when it returns to the initial position is v v t radicalbig v 2 + v 2 t , where v t is the terminal velocity which would be attained by a freely falling particle. [Hint: change the dependent variable in the differential equation from time t to distance z using dv/dt = ( dv/dz )( dz/dt ) = vdv/dz .] 2. Spherical polar coordinates ( r,θ,ϕ ) are defined by x = r sin θ cos ϕ, y = r sin θ sin ϕ, z = r cos θ, where r ≥ 0, 0 ≤ θ ≤ π and 0 ≤ ϕ ≤ 2 π . a. Using the chain rule, show that the vector d r = dx e x + dy e y + dz e z can be written as dr e r + rdθ e θ + r sin θdϕ e ϕ , where e r , e θ and e ϕ are unit vectors. Find the explicit form of these vectors on the basis e x ,...
View Full Document

## This homework help was uploaded on 02/24/2008 for the course PHYS 3318 taught by Professor Flanagan during the Spring '08 term at Cornell.

### Page1 / 2

hw1 - Physics 318 Problem Set 1 Due Wednesday 1 A particle...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online