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 on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 342 km/hourat an altitude of 775 m . 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 = 9.80 m/s2 .?
What is the speed v f of the package when it hits the ground?
Express your answer numerically in meters per second.??
Solution
vx = 342 km/h = 342 km/hr * (1 hr/3600 s) * (1000 m / 1 km) = 95 m/s
vyi = 0
Find the time it takes to fall 775 m
equation of motion:
hf = hi + vyi - 1/2*g*t^2
With hf = 0, vyi = 0, and hi = 775 m
0 = hi - 1/2*g*t^2
t = sqrt(2*hi / g)
Plug in numbers
t = sqrt(2*775 m / 9.80 m/s^2) = 12.58 s
The horizontal velocity doesn\'t change. Find the vertical velocity
vyf = vyi - g*t
vyf = 0 - 9.80 m.s^2 *12.58 s = -123.2 m/s
speed = sqrt(vx^2 + vyf^2) = 155.6 m/s
.
A relief airplane is delivering a food package to a group of people st.docx
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 on, and the only way to deliver the package is
by dropping it. The airplane flies horizontally with constant speed of 342 km/hourat an altitude
of 775 m . 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 = 9.80 m/s2 .?
What is the speed v f of the package when it hits the ground?
Express your answer numerically in meters per second.??
Solution
vx = 342 km/h = 342 km/hr * (1 hr/3600 s) * (1000 m / 1 km) = 95 m/s
vyi = 0
Find the time it takes to fall 775 m
equation of motion:
hf = hi + vyi - 1/2*g*t^2
With hf = 0, vyi = 0, and hi = 775 m
0 = hi - 1/2*g*t^2
t = sqrt(2*hi / g)
Plug in numbers
t = sqrt(2*775 m / 9.80 m/s^2) = 12.58 s
The horizontal velocity doesn't change. Find the vertical velocity
2. vyf = vyi - g*t
vyf = 0 - 9.80 m.s^2 *12.58 s = -123.2 m/s
speed = sqrt(vx^2 + vyf^2) = 155.6 m/s
