An airplane flies horizontally with a constant speed of 172.0 m/s at an altitude of 1390 m. a package is dropped out of the airplane. ignore air resistance. the magnitude of the gravitational acceleration is 9.8 m/s2. choose the right as positive x-direction. choose upward as positive y-direction keep 2 decimal places in all answers
(a) what is the vertical component of the velocity (in m/s) just before the package hits the ground? pay attention to the direction (the sign).
(b) what is the magnitude of the velocity (in m/s) (including both the horizontal and vertical components) of the package just before it hits the ground?

(a) - 165.032 m/s

(b) 238.37 m/s

Explanation:

initial horizontal velocity, ux = 172 m/s

height, h = 1390 m

g = 9.8 m/s^2

Let it strikes the ground after time t.

Use second equation of motion in vertical direction

-1390 = 0 - 0.5 x 9.8 x t^2

t = 16.84 second

(a) Let vy be the vertical component of velocity as it strikes the ground

Use first equation of motion in vertical direction

vy = uy - gt

vy = 0 - 9.8 x 16.84

vy = - 165.032 m/s

Thus, the vertical component of velocity as it strikes the ground is 165.032 m/s downward direction.

(b)

The horizontal component of velocity remains constant throughout the motion.

vx = 172 m/s

vy = - 165.032 m/s

The resultant velocity is v.

v = 238.37 m/s

Thus, teh velocity with which it hits the ground is 238.37 m/s.

the answer is c i did the same question so i know that's right!

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .