Example 10.42 from Elementary Algebra, 10.4 Solve Applications Modeled by Quadratic Equations

Solve Applications Modeled by Quadratic Equations: example 10.42

A firework is shot upwards with initial velocity 130 feet per second. How many seconds will it take to reach a height of 260 feet? Round to the nearest tenth of a second.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

An arrow is shot from the ground into the air at an initial speed of 108 ft/sec. 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.

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Step 1. Read the problem.
Step 2. Identify what we are looking for.		We are looking for the number of seconds, which is time.
Step 3. Name what we are looking for.		Let $t =$ the number of seconds.
Step 4. Translate into an equation.		Use the formula.
		$h = −16 t^{2} + v_{0} t$
Step 5. Solve the equation. We know the velocity $v_{0}$ is 130 feet per second.
The height is 260 feet. Substitute the values.
This is a quadratic equation, rewrite it in standard form.
Solve the equation using the Quadratic Formula.
Identify the a, b, c values.
Write the Quadratic Formula.
Then substitute in the values of a, b, c.
Simplify.
Rewrite to show two solutions.
Approximate the answers with a calculator.		$t \approx 4.6$ seconds, $t \approx 3.6$
Step 6. Check the answer. The check is left to you.
Step 7. Answer the question.		The firework will go up and then fall back down. As the firework goes up, it will reach 260 feet after approximately 3.6 seconds. It will also pass that height on the way down at 4.6 seconds.

Step 1. Read the problem.
Step 2. Identify what we are looking for.		We are looking for the number of seconds, which is time.
Step 3. Name what we are looking for.		Let $t =$ the number of seconds.
Step 4. Translate into an equation.		Use the formula.
		$h = −16 t^{2} + v_{0} t$
Step 5. Solve the equation. We know the velocity $v_{0}$ is 130 feet per second.
The height is 260 feet. Substitute the values.
This is a quadratic equation, rewrite it in standard form.
Solve the equation using the Quadratic Formula.
Identify the a, b, c values.
Write the Quadratic Formula.
Then substitute in the values of a, b, c.
Simplify.
Rewrite to show two solutions.
Approximate the answers with a calculator.		$t \approx 4.6$ seconds, $t \approx 3.6$
Step 6. Check the answer. The check is left to you.
Step 7. Answer the question.		The firework will go up and then fall back down. As the firework goes up, it will reach 260 feet after approximately 3.6 seconds. It will also pass that height on the way down at 4.6 seconds.

Solve Applications Modeled by Quadratic Equations: example 10.42

Solution

Your turn

Solve Applications Modeled by Quadratic Equations: example 10.42

Solution

Your turn