A stranded soldier shoots a signal flare into the air to attract the attention of a nearby plane. The flare has an initial vertical 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=v1t-16t^2

1. What is the maximum height that the flare reaches?

2. When will the flare reach that height?

3. At what time does the flare hit the ground again?

4. If the plane is flying at a height of 30,000 feet, a speed of 880 feet per second and is 50,000 feet from the fare when it is fired, will the flare hit it? If so, tell when this will happen. If not, tell when the flare reaches the planes altitude.

Question

Physics

Damarion

9 June, 19:33

A stranded soldier shoots a signal flare into the air to attract the attention of a nearby plane. The flare has an initial vertical 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=v1t-16t^2

1. What is the maximum height that the flare reaches?

2. When will the flare reach that height?

3. At what time does the flare hit the ground again?

4. If the plane is flying at a height of 30,000 feet, a speed of 880 feet per second and is 50,000 feet from the fare when it is fired, will the flare hit it? If so, tell when this will happen. If not, tell when the flare reaches the planes altitude.

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Answers (1)

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Midnight · Answer 1

h = ut - 16 t² = ut - 1/2 x32 t² = ut - 1/2 g t², g = acceleration = - 32 ft / s²

1) v² = u² - 2 g h, v = 0 so

h = u² / 2g = 1500² / 2 x 32 = 35156.25 ft

2) v = u - gt

t = u / g = 1500 / 32 = 46.875 s

3) It will hit the ground after 2 x 46.875 = 93.75 s

4) time to reach 30000 ft height t is given by

h = ut - 16 t²

30000 = 1500t - 16t²

16t²-1500t + 30000 = 0

t = 28.92 s and 64.82 s

Time required to travel 50000 by plane

= 50000/880 = 56.82. There is no match of timing so plane will not hit it.