Question

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 =—16t2+32t+6. How long is the baton in the air?

Answer 1

A drum major tosses a baton into the air and catches it and how long is the baton in the air is 22 feet

The heightis h of  a baton function of time is  t

h=−16t²+32t+6

dh/dt=d/dt(−16t²+32t+6)

=−32t+32

d²h/dt²=−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 feet

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