You drop a ball from a height of 98 feet. at the same time, your friend throws a ball upward. the polynomials represent the heights(in feet) of the balls after t seconds.

a)

b) See interpretation below

Step-by-step explanation:

a)

The motion of both balls is a free-fall motion: it means that the ball is acted upon the force of gravity only.

Therefore, this means that the motion of the ball is a uniformly accelerated motion, with constant acceleration equal to the acceleration of gravity:

in the downward direction.

For the ball dropped from the initial height of , the height at time t is given by

(1)

The ball which is thrown upward from the ground instead is fired with an initial vertical velocity , and its starting height is zero, so its position at time t is given by

(2)

Therefore, the polynomial that represents the distance between the two balls is:

b)

Now we interpret this polynomial, which is:

which represents the distance between the two balls at time t.

The interpretation of the two terms is the following:

- The constant term, , is the initial distance between the two balls, at time t=0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this problem,

- The coefficient of the linear term, , is the initial velocity of the second ball; this terms tells us that the distance between the two balls decreases every second by feet.

5

step-by-step explanation: