Chapter 6: Q47. (page 292)

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by $h (t) = - 16 t^{2} + 80 t + 200$ . Interpret the meaning of the y-intercept in the context of this problem.

Short Answer

Expert verified

The meaning of y-intercept is the height from which the object is fired at 0 seconds.

Step by step solution

Step 1. Given Information.

The given function is $h (t) = - 16 t^{2} + 80 t + 200$

Step 2. Use the concept.

The y-intercept is the point where the graph intersects they-axis.

Consider the function $f (x) = a x^{2} + b x + c, a \neq 0$ , the x-coordinate of vertex is $\frac{- b}{2 a}$ .

The Graph of $f (x) = a x^{2} + b x + c, a \neq 0$

opens up and has a minimum value when $a > 0$ , and
opens down and has a maximum value when $a < 0$

Step 3. Solution.

In the function $h (t) = - 16 t^{2} + 80 t + 200$ , we have $a = - 16, b = 80, c = 200$

So, the y-intercept is given by substituting $t = 0$

$\Rightarrow h (0) = - 16 {(0)}^{2} + 80 (0) + 200 = 200$

Which is the height from which the object is fired initially.

So, the meaning of y-intercept is the height from which the object is fired at 0 seconds.

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An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by $h (t) = - 16 t^{2} + 80 t + 200$ . Interpret the meaning of the y-intercept in the context of this problem.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Use the concept.

Step 3. Solution.

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An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by h(t)=-16t2+80t+200. Interpret the meaning of the y-intercept in the context of this problem.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Use the concept.

Step 3. Solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by $h (t) = - 16 t^{2} + 80 t + 200$ . Interpret the meaning of the y-intercept in the context of this problem.