While marching, a drum major tosses a baton into the air and catches it. The height #h# (in feet) of the baton after #t# seconds can be modeled by #h = —16t^2+32t+6#. How long is the baton in the air?

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Answer 1 · 2018-07-22T15:16:20

#22\ \text{feet}#

Given height #h# of baton as a function of time #t#

#h=-16t^2+32t+6#

#{dh}/dt=d/dt(-16t^2+32t+6)#

#=-32t+32#

#{d^2h}/{dt^2}=-32<0#

For maximum height #h#, we have

#{dh}/{dt}=0#

#-32t+32=0#

#t=1#

Setting #t=1# in the function of height, the maximum height of baton will be obtained at time #t=1# sec

#h(1)=-16(1)^2+32(1)+6#

#=22\ \text{feet}#