Show all your work. Answer the following questions. Correct answers without supp

Question

Show all your work. Answer the following questions. Correct answers without supporting work will not receive credit. Do not approximate any values and simplify you answers as much as possible. A dynamite blast blows a heavy rock straight up with a launch velocity of 160ft/sec. It reaches a height of s = 160 t - 16t^2 ft after t sec. What is the velocity? How high does the rock go? What are the velocity and speed of the rock when it is 256ft above the ground on the way up? On the way down? What is the acceleration of the rock at any time t during its flight? Evaluate the following limits: lim_x rightarrow 1 x^2 + x - 2/x^2 - x

Explanation / Answer

differentiate hegiht function w.r.t time to get velocity

a) it is equal to

160 - 32t at time t

b) height is maxmium when velocity = 0

i.e. t = 5 so height at t= 5 is

160 * 5 - 16*5*5 = 800 - 400 = 400

c) at height 256 we find time

160t - 16t^2 = 256

=> 10t - t^2 = 16

=>t^2 - 10t +16 = 0

(t -5)^2 = 9

t = 2 or t=8

t=2 going up velocity = 160 - 32*2 = 96

t = 8 going down = 160 - 32*8 = -96

d) acceleration

differentiate velocity w.r.t to

= -32

2) limit question

x^2 + x - 2 /x^2-x = (x+2)(x-1)/ x(x-1) = x+2/x = 3

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