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The height in feet of an arrow is modeled by the equation h(t)=(1+2t)(18-8t), where t is seconds after the arrow is shot. a. When does the arrow hit the ground? ◻ seconds b. From what height is the arrow shot? ◻ feet

The height in feet of an arrow is modeled by the equation h(t)=(1+2t)(18−8t) h(t)=(1+2 t)(18-8 t) , where t t is seconds after the arrow is shot.\newlinea. When does the arrow hit the ground? □ \square seconds\newlineb. From what height is the arrow shot? □ \square feet

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Q. The height in feet of an arrow is modeled by the equation h(t)=(1+2t)(18−8t) h(t)=(1+2 t)(18-8 t) , where t t is seconds after the arrow is shot.\newlinea. When does the arrow hit the ground? □ \square seconds\newlineb. From what height is the arrow shot? □ \square feet
  1. Find Ground Impact Time: First, let's find when the arrow hits the ground by setting h(t)h(t) to 00 and solving for tt. \newline0=(1+2t)(18−8t)0 = (1+2t)(18-8t)
  2. Solve for Time: Now, we need to find the values of tt that make the equation true. We can use the zero product property.\newlineSo, either (1+2t)=0(1+2t) = 0 or (18−8t)=0(18-8t) = 0.
  3. Check Validity of Time: Solving (1+2t)=0(1+2t) = 0 gives us t=−12t = -\frac{1}{2}, but that doesn't make sense because time can't be negative.
  4. Find Initial Height: Solving (18−8t)=0(18-8t) = 0 gives us t=188t = \frac{18}{8}, which simplifies to t=2.25t = 2.25. This is the time when the arrow hits the ground.
  5. Evaluate Initial Height: Now let's find the initial height from which the arrow is shot by evaluating h(t)h(t) at t=0t = 0.h(0)=(1+2×0)(18−8×0)h(0) = (1+2\times 0)(18-8\times 0)
  6. Evaluate Initial Height: Now let's find the initial height from which the arrow is shot by evaluating h(t)h(t) at t=0t = 0.h(0)=(1+2⋅0)(18−8⋅0)h(0) = (1+2\cdot 0)(18-8\cdot 0) Simplifying h(0)h(0) gives us h(0)=(1)(18)h(0) = (1)(18), which equals 1818 feet. So, the arrow is shot from a height of 1818 feet.

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