A ball is thrown upward form a height of 640 feet above the ground, with an init

Question

A ball is thrown upward form a height of 640 feet above the ground, with an initial velocity of 96 feet per second. From physics it is known that the velocity at time t is v(t) = 96 - 321 feet per second. a) Find s(t), the function giving the height of the ball at time t. b) How long will the ball take to reach the ball at time t. c) How high will the ball go? a) s(t) = b) The ball will reach the ground after seconds. c) The ball will go feet high. During weeks in a certain flu season, the rate at which the number of cases of influenza per 100,000 people in a country changed could be approximated by r'(t) = 3.432 e^0.10421 where I is the total number of people per 100,000 who have contracted influenza and t is time measured in weeks. Estimate I(t), the total number per 100,000 who have contracted influenza by time t. Assume that I(0) = 0. I(t) = Drilling of an oil well has a fixed cost of $80,000 and a marginal cost of M'(x) = 9000 + 40x dollars per foot, where x is the depth in feet. Find the expression for M(x), the total cost of drilling x feet.

Explanation / Answer

2)given velocity v(t)=96-32t ,s(0)=640

a)position s(t)=v(t) dt

s(t)=(96-32t) dt

s(t)=96t-16t2+c

s(0)=640

96*0-16*02+c=640

c =640

therefore s(t)=96t-16t2+640

b) on the ground height of ball is zero. s(t)=0

96t-16t2+640=0

-16(-6t+t2-40)=0

-16(t-10)(t+4)=0

t =10

ball reaches ground after 10 seconds

c)s(t)=96t-16t2+640

s(t)=-16(-6t+t2-40)

s(t)=-16(9-6t+t2-40-9)

s(t)=-16(9-6t+t2)+784

s(t)=-16(t-3)2+784

graph is open downwards,vertex is (3,784)

maximum height ball will go =784 feet

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