Astranded soldier shoots a signal flare into the air to attract the attention of a nearby plane. the flare has an initial velocity of 1500 feet per second. its height is defined by the quadratic function below. assume that the flare is fired from ground level. h=vit-16t^2 1. when will the fare reach 35,156.25 feet? ?   2.if the plane is flying at a height of 30,000 feet, a speed of 880 feet per second and is 50,000 feet fro the fare when it is fired, will the flare hit it? if so, tell when this will happen. if not, tell when the fare reaches the planes altitude.

1 . when will the fare reach that height:

The ascending and descending time are equal but let's show it: set the h = 0 

1500t - 16t^2 = 0 => solve the quadratic 

t = 0 => reject 

t = 375/4 seconds => period to hit the ground, notice that this is twice the time to reach max h. 

 

2. If the plane … solution:

d = vt 

t = d/v 

= 50,000/880 

It is approximately 56.8 sec to reach the flare but the flare reached max h at 375/8 ≈ 46.9 sec, so it won't hit the plane going up, but will it hit the plane on its way down from 35,156.25 ft.

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The answer is    (d) 7/2======we have    we also  have an integral      notice how function f splits up at x = 0. there's a left piece and a right pieceso we'll need to do the same thing with our integral: split it at x = 0we use a property of integrals that allows us to split up and sum:     notice that for the piecewise function f, the function has the equationf(x) = x when x  ≤ 0. so for the integral  , f(x) = x so it changes into      for the piecewise function f, the function has the equationf(x) = x+1  when x  > 0. for the integral  , we have    therefore, back to our splitted integral: