Question

The height in feet above the groundan arrow after it is shot can be modeledby y=16x2 +63 +4. Can the arow passOver a tree that is 68 feet tall? Explain

Answer 1

STEP 1

`\begin{gathered} y=-16x^2+63x+4 \\ (dy)/(dx)=-32x+63 \\ \\ At\text{ the maximum point }(dy)/(dx)=0 \\ \text{Hence} \\ 0=-32x+63 \\ 32x=63 \\ x=(63)/(32)=1.969 \\ \text{Step 2} \\ \text{substitute for x in the equation} \\ y=-16(1.969)^2+63(1.969)+4 \\ y_(\max )\approx66.02\text{ ft} \end{gathered}`

Since the maximum value of y is less than 68 ft, the height of the tree, then the arrow can not pass over the tree