Delivering a Package by Air (Figure 1) A relief airplane is delivering a food pa

Question

Delivering a Package by Air (Figure 1) A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land or. and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 220mph at an altitude of 800m ? The positive x and y directions are defined in the figure. For all parts, assume that the island refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80m/s2 . After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 220mph in the horizontal direction. Express your answer numerically in seconds. Neglect air resistance. If the package is to land right on the island, at what horizontal distance D from the plane to the island should the package be released? Express the distance numerically in meters. What is the speed of the package when it hits the ground? Express your answer numerically in miles per hour.

Explanation / Answer

v0 = 220 mph

h=800 m

a)

y = -0.5 g t^2 + voy t

-800 = -0.5*9.8 * t^2

t = 12.78

t = 12.8 s

b)

D = v0 t = (220*0.44704) * 12.78 = 1257 m = 1260 m

c)

vfx = 220*0.44704 = 98.3488 m/s

vfy = - g t = -9.8*12.78 = -125.244 m/s

v = sqrt(98.3488*98.3488+125.244*125.244) = 159 m/s

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.