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Finding the Time for a Firework to Reach 260 Feet
To find when a projectile reaches a given height, substitute the known values into the projectile motion formula () and solve for time ().
Problem: A firework is shot upward with an initial velocity of 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.
Solution: Substitute the initial velocity () and target height () into the formula:
Rewrite this quadratic equation in standard form by moving all terms to one side:
Identify the coefficients (, , ) and substitute them into the Quadratic Formula:
Simplify the expression:
Approximate the two solutions:
Unlike geometry applications where negative or secondary solutions might be discarded, both positive time values are valid here. The firework reaches 260 feet after approximately 3.6 seconds on the way up, and passes that height again at 4.6 seconds on the way down.
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Ch.10 Quadratic Equations - Elementary Algebra @ OpenStax
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Finding the Time for a Firework to Reach 260 Feet
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Learn After
As a pyrotechnics technician calculating the flight path of a firework, you find two positive time values for when the firework reaches a height of 260 feet. True or False: Both of these time values are physically meaningful for your safety report.
A pyrotechnics safety technician is documenting the flight of a firework shot at 130 feet per second. When solving for the time it takes to reach 260 feet, the technician identifies two positive solutions: 3.6 seconds and 4.6 seconds. According to the projectile motion model, what does the 4.6-second solution represent?
As a pyrotechnics safety technician, you are reviewing the trajectory data for a firework launched at 130 feet per second. Match each component of the projectile motion model to its physical interpretation in your safety report.
As a pyrotechnics safety technician, you must follow a standard procedural strategy to determine the exact moments a firework reaches a safety-critical height. Arrange the following steps in the correct order to solve for the time () using the projectile motion model.
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In a pyrotechnics trajectory report, a technician identifies two positive time solutions for a firework reaching a target height. This occurs because the firework passes the target height once while it is rising and a second time while it is ____.
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As a pyrotechnics safety officer, which standard algebraic formula do you use to model the height () in feet of a firework after () seconds, given its initial launch velocity ()?
A pyrotechnics safety technician is preparing to solve for the time () it takes a firework to reach a height of 260 feet. After rewriting the projectile motion equation into the standard quadratic form $16t^2 - 130t + 260 = 0, which values should the technician identify for the coefficientsa, b,c$ to use in the Quadratic Formula?