Question 614315: 1.A sprinter who average 30 ft/sec completed a race 1 sec before another sprinter who average 28 ft/sec. What was the distance of the race?
2. The average vertical speed of an experimental rocket is 1200 kph during its flight. Upon reaching its maximum height, it released a capsule which descended at an average vertical speed of 630kph. If the capsule touches the earth 90 min. after the rocket was launched, find the height reached by the rocket?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1.A sprinter who average 30 ft/sec completed a race 1 sec before another sprinter who average 28 ft/sec. What was the distance of the race?
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Faster runner DATA:
rate = 30 ft/sec ; distance = x ft ; time = x/30 seconds
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Slower runner DATA:
rate = 28 ft/sec ; distance = x ft ; time = x/28 seconds
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Equation:
slower runner time - faster runner time = 1 sec
x/28 - x/30 = 1 sec
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30x - 28x = 28*30
2x = 28*30
x = 14*30
x = 420 ft.
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2. The average vertical speed of an experimental rocket is 1200 kph during its flight. Upon reaching its maximum height, it released a capsule which descended at an average vertical speed of 630kph. If the capsule touches the earth 90 min. after the rocket was launched, find the height reached by the rocket?
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Rocket DATA:
h(t) = -16t^2+1200t
Max occurs at t = -b/(2a) = -1200/(-32) = 37.5 seconds
Max height = h(37.5) = -16(37.5)^2 + 1200*37.5 = 22500 k
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Time to descend = 22500/630 = 35.7 hr
Cheers,
Stan H.
Capsule DATA:
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