Aball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. it turns out that its motion can be broken down into its motion in the x-direction (horizontally) and its motion in the y-direction (vertically), and that those two components can be thought of completely independently. in other words, its horizontal motion has no influence on its vertical motion, and vice versa. i've written the two component functions here: x(t) is its position in the x-direction, and y(t) is its position in the y-direction. which of the following choices is correct? (ignore air resistance.) note: use a reference frame that makes all positions (x and y coordinates) of the projectile positive.

Step-by-step explanation:

Given that ball is thrown vertically with intial velocity 80 ft per second at a height of 15 feet off the ground.

Let angle of the ball thrown with horizontal be A

Then vertical velocity = 80 sinA

HOrizontal velocity = 80 cosA

Acceleration here is negative gravity

In fps system gravity g = -32ft/sec^2

s=ut+1/2at^2

Substitute to get

h(t) = 80cos A  t-16t^2 +15 (since initial height is 15 ft)

x(t) = 80 sin A t

the speed is   miles per hour > is false

step-by-step explanation:

we know that  

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

for the point

substitute the values of x and y

the linear equation is equal to

statements

case a) it takes hours to go miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

case b) the speed is   miles per hour

the statement is false

because the speed is

case c) the unit rate for the trip is

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took minutes to go the first miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct