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/second^{2}))

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**.

AdamTaurus
Nov 2, 2017

#1**+1 **

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