Question

An object is projected vertically upward with an initial velocity of $v_{0}$ ft/sec, and its distance $s(t)$ in feet above the ground after $t$ seconds is given by the formula $s(t)=-16 t^{2}+v_{0} t$ (a) If the object hits the ground after 12 seconds, find its initial velocity $v_{0}$ (b) Find its maximum distance above the ground.

          An object is projected vertically upward with an initial velocity of $v_{0}$ ft/sec, and its distance $s(t)$ in feet above the ground after $t$ seconds is given by the formula $s(t)=-16 t^{2}+v_{0} t$
(a) If the object hits the ground after 12 seconds, find its initial velocity $v_{0}$
(b) Find its maximum distance above the ground.

Added by Christina N.

Grade 6 Mathematics: Open Up Resources, Common Core State Standards Edition

N/A 6th Edition

Instant Answer

Solved by Expert Sheryl Ezze

06/07/2021

Step 1

Plugging in $t = 12$ and $s(t) = 0$, we get: $0 = -16(12)^2 + v_{0}(12)$ $0 = -16(144) + 12v_{0}$ $0 = -2304 + 12v_{0}$ $12v_{0} = 2304$ $v_{0} = \frac{2304}{12}$ $v_{0} = 192$ Show more…

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An object is projected vertically upward with an initial velocity of $v_{0}$ ft/sec, and its distance $s(t)$ in feet above the ground after $t$ seconds is given by the formula $s(t)=-16 t^{2}+v_{0} t$ (a) If the object hits the ground after 12 seconds, find its initial velocity $v_{0}$ (b) Find its maximum distance above the ground.