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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.

Nov 2, 2017

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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

Nov 2, 2017