ian tosses a bone up in the air for his dog, spot. the height, h, in feet, that spot is above the ground at…

ian tosses a bone up in the air for his dog, spot. the height, h, in feet, that spot is above the ground at the time t seconds after she jumps for the bone can be represented by the function $h(t)=-16t^{2}+20t$. what is spots average rate of ascent, in feet per second, from the time she jumps into the air to the time she catches the bone at $t = \frac{1}{2}$ second? enter your answer in the box.

ian tosses a bone up in the air for his dog, spot. the height, h, in feet, that spot is above the ground at the time t seconds after she jumps for the bone can be represented by the function $h(t)=-16t^{2}+20t$. what is spots average rate of ascent, in feet per second, from the time she jumps into the air to the time she catches the bone at $t = \frac{1}{2}$ second? enter your answer in the box.

Answer

Explanation:

Step1: Find the height at $t = 0$

When $t = 0$, $h(0)=-16\times0^{2}+20\times0 = 0$.

Step2: Find the height at $t=\frac{1}{2}$

$h(\frac{1}{2})=-16\times(\frac{1}{2})^{2}+20\times\frac{1}{2}=-16\times\frac{1}{4} + 10=-4 + 10=6$.

Step3: Calculate the average rate of ascent

The average rate of ascent is $\frac{h(\frac{1}{2})-h(0)}{\frac{1}{2}-0}$. Substitute $h(0) = 0$ and $h(\frac{1}{2})=6$ into the formula: $\frac{6 - 0}{\frac{1}{2}}=12$.

Answer:

12