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# Word Problems

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Larry uses a slingshot to launch a rock straight up from a point 6 ft above level ground with an initial velocity of 170 ft/sec. Use the fact that $$h(t)=-\frac{1}{2}gt^2+v_0t+h_0$$. (where g is the acceleration due to gravity (-32 feet/second2))

a) Find an equation that models the height of the rock t seconds after it is launched.

I'll make this one a bit easier by confidently saying that the equation is $$h(t)=-16t^2+170t+6$$.

b) What is the maximum height of the rock? When will it reach that height? Determine the answer algebraically.

c) When will the rock hit the ground? Determine the answer algebraically.

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Max ht will occur at the vertex

x coordinate of the vertex is    -170 / [2 * -16]  = 5.3125 = seconds to reach max ht

Max ht  = -16 [5.3125]^2  +  170 [5.3125] + 6  ≈ 457.6  ft

It will reach the ground  when h = 0

-16 [t]^2  +  170 [t] + 6  =  0

-8t^2  + 85t + 3  = 0

Sub into quadratic formula      a = -8  b= 85   c = 3

Solving this...it will hit the ground  at ≈ 10.66 sec  after launch

CPhill  Nov 2, 2017

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