1)It has been conjectured that a fish swimming a distance of L ft at a speed of V ft/sec relative to the water and against a current flowing at the rate of U ft/sec (u<v) expends a total energy given by: E(v)= aLv^3/v-u

where E is measured in foot-pounds (ft-lb) and a is a constant. Find the speed V at which the fish must swim in order to minimize the total energy expended.

2) By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 15in long and 8 in wide, find the dimensions of the box that will yield the maximum volume,

3) In an open box has a square base and volume of 108 cubic inches, and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amoun o material is used in construction.

4) A grain silo has the shape of a right circular cylinder surronded by a hemisphere. If the Silo is to have a capacity of 504*PI cubic feet, find the radius and height of the silo that requires the least amount of material to construct.
(The volume of the silo is pi*r^2*h + 2/3*pi*r^3, and the surface area, including the floor, is pi(3*r^2 + 2*r*h)

A rocket in outer space that is moving at a speed of 1.50 km/s relative to an observer fires its motor. Hot gases are expelled out the rear at 2.55 km/s relative to the rocket. What is thespeed of the gases relative to the observer?

A spaceship moves away from Earth at a speed 0.874c and fires a shuttle craft that then moves in a forward direction at 0.21c relative to the ship. The pilot of the shuttle launches a probe forward at a speed of 0.412c relative to the shuttle.
Determine thespeed of the shuttle relative to Earth. Answer in units of c.
Part

A child in an airport is able to cover 270 meters in 3 minutes running at a speed down a moving sidewalk in the direction of the sidewalks motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 256 meters in 4 mintues. What is the child's running speed and the she spe

A 45.5 kg girl is standing on a plank that has a mass of 143 kg. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless supporting surface. The girl begins to walk along the plank at a constant speed of 1.41 m/s relative to the plank.
(a) What is her speedrelative to the ice surface?

Tom's rocket ship is moving away from Kathy at 0.75c. He fires a laser beam in the backward direction, toward Kathy. According to Galilean relativity. How fast does the laser beam move relative to Kathy, assuming that Tom observes the beam to move away from him at speed c? How fast according to Einstein's relativity? Why?

Bonnie drove 540 miles in three times the time it took Buffy to travel 135 miles. Buffy's speed was slower than Bonnie's by 15 miles per hour. Findthe rate and time of each.

Kim starts to walk 3 mi to school at 7:30 a.m. with a temperature of 0 degrees F. Her brother Bryan starts at 7:45 a.m. on his bicycle, traveling 10 mph faster than Kim. They they get to school at the same time, then how fast is each one traveling?

In a certain region, pesticide can be sprayed from an iairplane only if the temperature is at least 70 degrees, therelative humidity is between 15 and 35%, and the wind speed is at most 10 miles per hour,

Calculate therelativespeed of a 64-bit adder using ripple carry only, a ripple carry of 4-bit groups that use carry lookahead, and a ripple carry of 16-bit groups that use carry lookahead. Use the simulator located at the following url:
http://www.ecs.umass.edu/ece/koren/arith/simulator/
Also explain, what is relative spee

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1. The launch catapult of an aircraft carrier gives the 7Mg jet airplane gives the airplane a constant acceleration and launches the airplane in a distance of 100 m measured along the angled takeoff ramp. The carrier is moving at a constant speed of 16 m/s. If an ab