Question

A pizza chef tosses dough into the air to make his famous light and fluffy pizza crust. The equation h(t) = –16t^2 + 16t+4 relates h, the height of the dough in feet, and t, the time in seconds. The chef tosses the dough from a height of 4 feet at t=0 seconds and catches the dough again at a height of 4 feet. The graph below shows the equation h(t) = -16t^2 + 16 + 4.after being tossed by the chef, how much higher did the dough travel into the air?A.2 ftB.4 ftC.6 ft D .8 ft

Answer 1

Consider the equation,

`h(t)=-16t^2+16t+4`

When the dough reaches the maximum height, the speed of the dough must become zero. Also we know that the velocity or speed is given by the first derivative of height,

`h^(\prime)(t)=0\Rightarrow-32t+16=0\Rightarrow t=0.5`

Thus, the dough reaches its maximum height at time 0.5 seconds.

Solve for the height at instant of 0.5 seconds,

`h(0.5)=-16(0.5)^2+16(0.5)+4=-4+8+4=8`

Thus, the maximum height travelled by the dough is 8 feet.

Therefore, option (D) is the correct choice.