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

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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 ,...
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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.

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

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