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 300 feet over level terrain drops a supply package. (a) How long will it take until the supply package strikes the ground? (Round your answer to three decimal places.) t = sec (b) The aircraft is flying at 146 miles per hour. How far will the supply package travel horizontally during its descent? (Round your answer to one decimal place.) ft

Answer 1

(a). The speed of the aircraft has not been mentioned. We will, therefore , presume that v₀ = 0 ( as the package has been dropped and not thrown). Also, s₀ = 300 ft. The supply package will strike the ground when s = 0 i.e. when -16t² +300 = 0 or, 16t² = 300 or, t² = 300/16 = 75/4. Then t = 5?3/2 = 4.33 seconds (approximately). Thus, the supply package will strike the ground in 4.33 seconds.

(b). Here, v₀ =146 mph. Hence s = -16t² +146t+300 The supply package will strike the ground when s = 0 i.e. when -16t²+146t+ 300=0. A graph of this function (downwards opening parabola) is attached. However, this only indicates the time (10.8 )seconds when the package will strike the ground. The information provided is not adequate to determine the horizontal distance that the supply package will travel when it hits the ground.