Jalen S.

asked • 02/23/24

solving a word problem using quadratic equation with irrational roots

A model rocket is launched with an initial upward velocity of 60/ms

. The rocket's height h

 (in meters) after t

 seconds is given by the following.

=h−60t5t2

Find all values of t

 for which the rocket's height is 27

 meters.

Round your answer(s) to the nearest hundredth.



  1. ive been stuck on this topic for two day, please break down why you did what specific step to get the answer

Mark M.

Formula given is incorrect. Repost with correct information.
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02/23/24

1 Expert Answer

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James S. answered • 02/23/24

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There is something wrong with your equation.


You should have something like h(t) = a + 60t - 9.8t2.


The rocket's upward velocity should be positive. The acceleration due to gravity (bringing the rocket back to earth) should be negative.


What is the initial height (above) ground (a)? Zero?



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Randall M.

You're absolutely right, there was an error in the equation provided. The typical model rocket equation includes: Initial height (a): This is the initial height of the rocket above the ground at t = 0 seconds. It can be zero if launched from the ground. Initial velocity (v): This is the initial upward velocity of the rocket in meters per second, which should be positive. Acceleration due to gravity (g): This is a constant negative value representing the acceleration caused by gravity pulling the rocket back down, typically -9.8 m/s². Therefore, the corrected equation representing the rocket's height is: h(t) = a + vt - 0.5 * g * t^2 where: a: Initial height (unknown in this case) v: Initial velocity (60 m/s) g: Acceleration due to gravity (-9.8 m/s²) t: Time in seconds h(t): Height of the rocket at time t Solving for a: Since the problem asks for the initial height (a), we need to find it when t = 0. Substitute these values into the corrected equation: h(0) = a + v(0) - 0.5 * g * (0)^2 27 = a + 0 - 0 (since the rocket doesn't move at t = 0 and g(0) = 0) Therefore, the initial height of the rocket is 27 meters. Finding the time (t) when the height is 27 meters: Now, substituting h(t) = 27 and a = 27 in the corrected equation: 27 = 27 + 60t - 0.5 * 9.8 * t^2 Solving this quadratic equation will give us the values of t for which the height is 27 meters. However, the provided equation has irrational roots (roots that cannot be expressed as a simple fraction or decimal). Therefore, you'll need to use a calculator to find the approximate solutions and round them to the nearest hundredth. Remember, since the height cannot be negative, only the positive solution (if any) will be relevant in this context.
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02/24/24

James S.

tutor
You do not need a calculator to find the exact solution(s). The quadratic formula will give you the exact solution(s).
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02/24/24

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