question 7 (4 points) the height, h, of a stomp rocket (propelled by a short blast of air) above the ground…

question 7 (4 points) the height, h, of a stomp rocket (propelled by a short blast of air) above the ground after t seconds is given by the equation h(t)=−16t + 100t + 5. here is a graph that represents height above ground (feet) time (seconds) what is the y - intercept represented by in the equation? what initial velocity of the rocket? ft/sec when does the rocket hit the ground (round to the nearest integer)? between and seconds blank 1: blank 2: blank 3: blank 4:

question 7 (4 points) the height, h, of a stomp rocket (propelled by a short blast of air) above the ground after t seconds is given by the equation h(t)=−16t + 100t + 5. here is a graph that represents height above ground (feet) time (seconds) what is the y - intercept represented by in the equation? what initial velocity of the rocket? ft/sec when does the rocket hit the ground (round to the nearest integer)? between and seconds blank 1: blank 2: blank 3: blank 4:

Answer

Explanation:

Step1: Find the y - intercept

The equation of the height is $h(t)=-16t^{2}+100t + 5$. The y - intercept is found when $t = 0$. Substitute $t=0$ into the equation: $h(0)=-16(0)^{2}+100(0)+5 = 5$.

Step2: Find the initial velocity

The general form of the height - time equation for vertical motion is $h(t)=-16t^{2}+v_{0}t+h_{0}$, where $v_{0}$ is the initial velocity and $h_{0}$ is the initial height. Comparing with $h(t)=-16t^{2}+100t + 5$, the initial velocity $v_{0}=100$ ft/sec.

Step3: Find when the rocket hits the ground

Set $h(t)=0$, so we have the quadratic equation $-16t^{2}+100t + 5=0$. Using the quadratic formula $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ for a quadratic equation $ax^{2}+bx + c = 0$. Here, $a=-16$, $b = 100$, and $c = 5$. First, calculate the discriminant $\Delta=b^{2}-4ac=(100)^{2}-4\times(-16)\times5=10000 + 320=10320$. Then $t=\frac{-100\pm\sqrt{10320}}{-32}=\frac{-100\pm101.597}{-32}$. We get two solutions: $t_{1}=\frac{-100 + 101.597}{-32}\approx - 0.05$ and $t_{2}=\frac{-100-101.597}{-32}\approx6.3$. We discard the negative solution. Rounding to the nearest integer, $t = 6$ seconds.

Answer:

Blank 1: 5 Blank 2: 100 Blank 3: 6 Blank 4: N/A (no fourth - blank question given in the problem statement)