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.
Accepted Solution
A:
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 functionRemember thatThe t-intercept of the function is the value of t when the value of function h(t) is equal to zerosoequate 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]