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

a) 17.667 s

b) 4094 feet

Explanation:

a) The position equation of the model is given by:

`s=-16t^2+v_ot+s_o\\\\v_o=initial \ velocity = 158\ miles/hour\\\\s_o=Initial\ height=900\ ft\\\\1 \ mile = 5280\ ft, 1\ hour= 3600\ s\\\\Therefore:\\\\v_o=158\ miles/hour = 158*(5280)/(3600)=231.733\ ft/s\\ \\Substituting:\\\\0=-16t^2+231.733t+900\\\\16t^2-231.733t=900\\\\\\16t^2-231.733-900=0\\\\Solving\ the\ quadratic\ equation\ gives:\\\\ t=17.667\ s\ or \ t=-3.184\ s\\\\Since\ the \ time\ cannot\ be\ negative\ therefore\ t=17.667\ s`

b) The horizontal distance = Initial velocity × time = 231.733 × 17.667 = 4094 feet