+895 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.
+128406 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
