You are trying to find out how high you have to pitch a water balloon in order for it to burst when it hits the ground. you discover that the balloon bursts when you have pitched it to a height of 11 m. with what velocity did the balloon hit the ground? the acceleration of gravity is 9.8 m/s^2. the positive direction is up, so the velocity when it hits is negative.

Step-by-step explanation:

So, as balloon reaches its maximum height i.e. 11 m , its velocity become 0.

Therefore, .

It is given that acceleration due to gravity should be taken as , .(because it direction is down)

Now it is also given that upward direction is positive and downward direction is negative. So velocity should be negative.

Using equation of motion,

  .....eqn 1.

where , displacement = -11 m(because it displace towards down) and

Putting these values in eqn 1 .

But as we know direction of velocity is downward.

Therefore,

where negative sign indicates its direction is downward.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.