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(1 point) A coin, thrown upward at time t = 0 from an office in the Empire State Building, has height in feet above the ground t

seconds later given by

h(t) = -16t2 + 48t+448 = -16(t – 7)(t + 4).

(a) From what height is the coin thrown? Include units in your answer. 512 feet

help (units)

(b) At what time does the coin hit the ground? Include units in your answer.

help (units)

Respuesta :

MrRoyal

Answer:

The coin was thrown from 448 feet

Time to hit the ground is 7 seconds

Step-by-step explanation:

Given

[tex]h(t) = -16(t - 7)(t + 4)[/tex]

Solving (a): Height when coin is thrown

At this point t = 0

So, we have:

[tex]h(0) = -16(0 - 7)(0 + 4)[/tex]

Solve expressions in the brackets

[tex]h(0) = -16(-7)(4)[/tex]

[tex]h(0) = 448[/tex]

Hence, the coin was thrown from 448 feet

Solving (b): Time to hit the ground

At this point, h = 0.

So, we have:

[tex]0 = -16(t - 7)(t + 4)[/tex]

Reorder

[tex]-16(t - 7)(t + 4) = 0[/tex]

Divide both sides by -16

[tex](t - 7)(t + 4) = 0[/tex]

This gives:

[tex]t - 7 = 0[/tex]      or      [tex]t + 4 = 0[/tex]

[tex]t = 7[/tex]   or     [tex]t = -4[/tex]

Since, time can't be negative;

[tex]Time = 7\ seconds[/tex]

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