Suppose a football is kicked with an initial velocity of 82 ft/sec., at an angle of

58° to the ground. what is the position of the ball after two seconds?

(remember: acceleration due to gravity is 32 ft/s².) round your answer

to the nearest whole foot. show all work.

The position P is:

ft     Remember that the position is a vector. Observe the attached image

Step-by-step explanation:

The equation that describes the height as a function of time of an object that moves in a parabolic trajectory with an initial velocity is:

Where is the initial height = 0 for this case

We know that the initial velocity is:

82 ft/sec at an angle of 58 ° with respect to the ground.

So:

ft/sec

ft/sec

Thus

The height after 2 sec is:

Then the equation that describes the horizontal position of the ball is

Where

for this case

ft / sec

ft/sec

So

After 2 seconds the horizontal distance reached by the ball is:

Finally the vector position P is:

ft

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.