Manny is repairing a window air conditioning unit on the 11th floor of a building and is approximately 98 off the ground. While working, Manny drops his screwdriver. The height (h) of the screwdriver in feet after t secounds of falling from the 11th floor is modeled by the function h= -16^2 + 98. How long will it take for the screwdriver to reach the ground? Round to the nearest tenth if neccesary.

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calculista calculista · Answer 1 · 2019-03-21T00:00:45+01:00

Answer:

[tex]t=2.5\ seconds[/tex]

Step-by-step explanation:

we have

[tex]h=-16t^{2} +98[/tex]

To find out how long it will take for the screwdriver to reach the ground, find the t-intercept of the function

Remember that

The t-intercept of the function is the value of t when the value of function h(t) is equal to zero

so

equate the function h(t) to zero and solve the quadratic equation

[tex]-16t^{2} +98=0[/tex]

Solve for t

[tex]16t^{2}=98[/tex]

Divide by 16 both sides

[tex]t^{2}=6.125[/tex]

square root both sides

[tex]t=2.5\ seconds[/tex]