Question

Use the position equation given below, where s represents the height of the object (in feet), v0 represents the initial velocity of the object (in feet per second), s0 represents the initial height of the object (in feet), and t represents the time (in seconds), as the model for the problem. s = −16t2 + v0t + s0 An aircraft flying at 900 feet over level terrain drops a supply package.

(a) How long does it take until the supply package to strike the ground? (Round your answer to three decimal places.) t = sec

(b) The aircraft is flying at 158 miles per hour. How far does the supply package travel horizontally during its descent? (Round your answer to one decimal place.) ft

Answer 1

Answer:

(a) 7.5 seconds

(b) The horizontal distance the package  travel during its descent is 1737.8 ft

Step-by-step explanation:

(a) The given function for the height of the object is s = -16·t² + v₀·t + s₀

The initial height of the object s₀ = 900 feet

The initial vertical velocity of the object v₀$_y$ = 0 m/s

The time it takes the package to strike the ground is found as follows;

0 = -16·t² + 0×t + 900

900 = 16·t²

t² = 900/16 = 62.25

t = √62.25 = 7.5 seconds

(b) Given that the horizontal velocity of the package is given as 158 miles/hour, we have

158 miles/hour = 231.7126 ft/s

The horizontal distance the package  covers in the 7.5 second of vertical flight = 231.7126 ft/s × 7.5 s = 1737.8445 feet = 1737.8 ft to one decimal place

The horizontal distance the package  travel during its descent = 1737.8 ft.