Question 1142427: A Weather sensor is shot from a platform into the air and allowed to fall back to the ground. Its height in meters is given by the equation h= -49t^2 + 18t + 5, where t is the time in seconds.
a) What is the maximum height of the sensor, and at what time does it occur?
b) When does the Rocket return to the ground?
c) At what times is the sensor 15 meter above the ground?
d) How high is the sensor after 1.5 seconds?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A Weather sensor is shot from a platform into the air and allowed to fall back to the ground. Its height in meters is given by the equation h= -49t^2 + 18t + 5, where t is the time in seconds.
a) What is the maximum height of the sensor, and at what time does it occur?
Max height is the vertex of the parabola, at t = -b/2a
t = -18/-98 = 9/49 seconds.
h(t) = -49t^2 + 18t + 5
h(9/49) = -49*(81/2401) + 18*9/49 + 5
= -81/49 + 162/49 + 245/49
= 336/49 = 48/7 meters
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b) When does the Rocket return to the ground?
When h(t) = 0
-49t^2 + 18t + 5 = 0
Solve for t
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c) At what times is the sensor 15 meter above the ground?
At no time.
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d) How high is the sensor after 1.5 seconds?
Find h(1.5)
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The function is probably h(t) = -4.9t^2 + 18t + 5, not 49t^2
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If so, do the same calculations using 4.9.
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