A rocket is launched from the surface of the Earth with an initial velocity of 300 m/s upward. The rocket's acceleration due to gravity is approximately 9.8 m/s29.8m/s2, and it is also subject to air resistance, which can be modeled by the equation �air=−��Fair​=−kv, where �airFair​ is the air resistance force in newtons, �k is a positive constant, and �v is the velocity of the rocket in m/s. Source: helpinhomework.org 

a) Determine the rocket's velocity as a function of time, �(�)v(t), given that the air resistance is proportional to its velocity.

b) Find the time it takes for the rocket to reach its maximum height.

c) Calculate the maximum height the rocket reaches above the Earth's surface.

d) Determine the rocket's velocity as a function of time on its way down to the Earth, taking into account the air resistance.

e) Find the time it takes for the rocket to return to the surface.

f) Calculate the total time of flight for the rocket.

Fogerty Company makes two products, titanium Hubs and Sprockets.Data regarding the two products follow:

The Smiths Falls Times assembles sports watches. The watchesconsist of three main components, Quartz mechanism, the case andthe strap. SFC sources components from outside and assembles thewatches in its factory.

Extensive customer survey have established that there are threemain functions for the watches in the niche that SFT has chosen;time, water resistance and style. Time is provided by the quartzmechanism; water resistance and style are provided by the case adthe strap. Replaceable batteries power all the watches. However,once the case is opened to replace the waterproof nature of thewatch is usually lost.

Market surveys have established three price points for the threenew watches that SFT now has in its design stage: (1) $30 for abasic watch (2) $50 for a basic chronograph and (3) $120 for amultifunctional watch. SFT ha determined, given itsfacility-sustaining costs and its cost of capital, that threewatches must provide a margin of $4, $8 and $15 to beacceptable.

Based on initial specification the supplier of quartz mechanismshas quoted price of $8, $15 and $40 for the three watches. Becausethese mechanisms use standard components and well-known technology,planners at SFT consider these costs to be as low as they can be.The implication is that any needed target cost reduction will notbe wrung out of the quartz mechanism.

There are many sources for the wrap straps, and the prices varywidely based functionality, which include appearance, compositionand wear. Suppliers’ quoted price ranges for the three watches areas follows: $2-$7, $6-$9 and $20-$30. For any given level offunctionality chosen there is little price variation amongsuppliers because the watchstraps are commodity products producedcost effectively.

The case provides two critical functions – style and waterresistance. All cases have to be guaranteed to a depth of 50mminimums and customer focus group show that they find a guaranteeddepth of 100 meters more desirable. Depending upon style and degreeof water resistance the supplier quoted the following price rangesfor the watchcases: $5 -$15, $10 - $25 and $20 - $35. Both styleand water resistance increased in the product price.

Conversations with factory personnel indicated that theestimated costs of assembling, packaging, and shipping each watchwere about $5, $7 and $15. For an investment estimated at about$5,000,000 SFT could provide management advice to one of itssuppliers. This advice would be related to developing bettermanufacturing methods. These improved methods would likely reducethe cost of each case supplied by about 25%.

Required:

a) Compute the cost ranges for the three watches

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b) Identify how you would choose the specific strap and case foreach watch.

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c) How would you decide whether to make the investment toimprove the efficiency of the case supplier?

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d) Factory personnel indicate that for an investment of about$10,000,000 the existing factory layout could be altered toaccommodate more-efficient production. The result would be toreduce assembly, packaging and shipping costs by about $2 per unit.How would you decide whether to make this investment?