Use the position equation s = −16t2 + v0t + s0 as the model for the problem.A cargo plane flying at 9000 feet over level terrain drops a 400-pound supply package.(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.) sec(b) The plane is flying at 700 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)
Question
Use the position equation s = −16t2 + v0t + s0 as the model for the problem.A cargo plane flying at 9000 feet over level terrain drops a 400-pound supply package.(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.) sec(b) The plane is flying at 700 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)
Solution
(a) To find out how long it will take the package to strike the ground, we need to set the position equation equal to zero and solve for t (time). The initial velocity (v0) of the package is 0 (since it's dropped, not thrown), and the initial height (s0) is 9000 feet. So the equation becomes:
0 = -16t^2 + 0*t + 9000
Solving for t gives us:
16t^2 = 9000 t^2 = 9000 / 16 t = sqrt(562.5) t = 23.73 seconds (rounded to two decimal places)
(b) To find out how far the package will travel horizontally during its descent, we need to convert the plane's speed from miles per hour to feet per second, since the vertical distance was given in feet and the time in seconds. There are 5280 feet in a mile and 3600 seconds in an hour, so:
700 miles/hour = 700 * 5280 / 3600 = 1029.33 feet/second
Then, we multiply this speed by the time it takes for the package to hit the ground:
1029.33 feet/second * 23.73 seconds = 24414.24 feet (rounded to two decimal places)
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