The equation D=\sqrt{2h} can be used to approximate the distance D, in miles, that a person can see to the horizon from a height h, in feet. a) How far to the horizon can you see through an airplane window at a height of 28,000 feet? b) Carrie can see about 261 miles to the horizon through an airplane window. How high is the airplane?

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answer with steps would be appreciated

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rosewolf781

Horizon

If you are looking at the horizon, you can determinethe distance you are from the horizon in miles, D, froma height, h, in feet by the equation of D = . If you are standing on a mountain topthat is 12,000 feet in elevation, how far are you fromthe horizon?

To earn full credit, show how you solved the problemby using correct mathematical symbols and by explainingthoroughly in words each step.

Matt and his friends are enjoying an afternoon at a baseball game. A batter hits a towering homerun, and
Matt shouts, âWow, that must have been 110 feet high!â The ball was 4 feet off the ground when the batter
hit it, and the ball came off the bat traveling vertically at 80 feet per second.

a. Model the ballâs height h (in feet) at time t (in seconds) using the projectile motion model h(t) = 16t2 + v0t + h0 where v0 is the projectileâs initial vertical velocity (in feet per second) and h0 is the projectileâs initial height (in feet). Use the model to write an equation based on Mattâs claim, and then determine whether Mattâs claim is correct.

b. Did the ball reach a height of 100 feet? Explain.

c. Let hmax be the ballâs maximum height. By setting the projectile motion model equal to hmax, show
how you can find hmax using the discriminant of the quadratic formula.

d. Find the time at which the ball reached its maximum height.

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