Chapter 10: Q 10.83 (page 1205)

An arrow is shot from the ground into the air at an initial speed of $108 f t / s e c$ .Use the formula $h = - 16 t^{2} + v_{0} t$ to determine when the arrow will be 180 feet from the ground . Round the nearest tenth of a second .

Short Answer

Expert verified

The result is 3.7 seconds and 3 seconds.

Step by step solution

Given information

The given statement in which an arrow is shot from the ground into the air at an initial speed of $108 f t / s e c$ .

The height is 180 feet.

Simplify the equation

$h = - 16 t^{2} + v_{0} t$

The velocity $v_{0}$ is 108 feet per second and height is 180 feet.

Substitutes the values into the equation .

$180 = - 16 t^{2} + 108 t 16 t^{2} - 108 t + 180 = 0 s i m p l i f y t h e e q u a t i o n 4 t^{2} - 27 t + 45 = 0$

Using quadratic formula to simplify the equation

a = 4 , b = -27 and c= 45

$t = \frac{- (- 27) \pm \sqrt{{(- 27)}^{2} - 4 (4) (45)}}{2 \times 4} t = \frac{27 \pm \sqrt{729 - 720}}{8} t = \frac{27 \pm \sqrt{9}}{8} t = \frac{27 + 3}{8}, \frac{27 - 3}{8} t = 3.7, 3$

At 3.7 seconds as well as at 3 seconds the arrow will be 180 feet from the ground .

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An arrow is shot from the ground into the air at an initial speed of $108 f t / s e c$ .Use the formula $h = - 16 t^{2} + v_{0} t$ to determine when the arrow will be 180 feet from the ground . Round the nearest tenth of a second .

Short Answer

Step by step solution

Given information

Simplify the equation

Using quadratic formula to simplify the equation

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An arrow is shot from the ground into the air at an initial speed of108ft/sec.Use the formula h=-16t2+v0tto determine when the arrow will be 180 feet from the ground . Round the nearest tenth of a second .

Short Answer

Step by step solution

Given information

Simplify the equation

Using quadratic formula to simplify the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

An arrow is shot from the ground into the air at an initial speed of $108 f t / s e c$ .Use the formula $h = - 16 t^{2} + v_{0} t$ to determine when the arrow will be 180 feet from the ground . Round the nearest tenth of a second .