a rocket is fired straight upward from ground level with an initial velocity of 480Km)hr. After t second , its distance above the ground level is given by 480t-16t^2. For what time interval is the rocket more than 3200Km above ground level?
Answer:
answer
Explanation:
The rocket is 19.5 m above the ground when h=19h=19:
h19.50tttamp;=−8t2+32tamp;=−8t2+32tamp;=−8t2+32t−19.5amp;=−32±322−4(−8)(−19.5)−−−−−−−−−−−−−−−−√2(−8)amp;=−32±1024−624−−−−−−−−−√−16amp;=−32±400−−−√−16amp;=−32±20−16amp;=−32+20−16=0.75amp;=−32−20−16=3.25amp;amp;amp;amp;amp;amp;amp;amp;Substitute h=19.amp;Subtract 19.5 on both sides.amp;Solve for t using the Quadratic Formula.amp;Simplify.amp;Subtract.amp;Evaluate the root.amp;Find the two solutions.
h
19.5
0
t
t
t
amp;=−8t
2
+32t
amp;=−8t
2
+32t
amp;=−8t
2
+32t−19.5
amp;=
2(−8)
−32±
32
2
−4(−8)(−19.5)
amp;=
−16
−32±
1024−624
amp;=
−16
−32±
400
amp;=
−16
−32±20
amp;=
−16
−32+20
=0.75
amp;=
−16
−32−20
=3.25
amp;
amp;
amp;
amp;
amp;
amp;
amp;
amp;Substitute h=19.
amp;Subtract 19.5 on both sides.
amp;Solve for t using the Quadratic Formula.
amp;Simplify.
amp;Subtract.
amp;Evaluate the root.
amp;Find the two solutions.
The rocket will then be at least 19.5 m above the ground for the interval 0.75≤t≤3.25
0.75≤t≤3.25
The time interval for which the rocket is more than 3200 km above the ground level is 61.25 seconds.
What is quadratic equation?To solve this problem, we need to find the time interval for which the rocket's distance above the ground level is greater than 3200 km.
We can start by setting the equation for the rocket's distance above the ground level equal to 3200:
We can then solve this equation for t using the quadratic formula
[tex]480t - 16t^2 = 3200\\t = (-480 +/- sqrt(480^2 - 4*(-16)*3200)) / (-32)\\This simplifies to:\\t = (-480 +/- sqrt(480^2 + 256000)) /\\ (-32)t = (-480 +/- sqrt(2304000)) /\\ (-32)t = (-480 +/- 1500) / (-32)t = (-1980) /\\(-32)t = 61.25t = -24.25\pi[/tex]
Since the time interval we are looking for is positive, we can ignore the negative solution. The time interval for which the rocket is more than 3200 km above the ground level is therefore 61.25 seconds.
Learn more about quadratic equation, here:
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Answer:
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Explanation:
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mRNA
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Answer:
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