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?
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.