The path of a basketball can be modeled by the equation h(d)=-0.13d^2+d+2. where h(d) is the height in meters or the basketball and d is the horizontal distance in meters from the player. How far does the ball travel horizontally before hitting the floor?

You need to find the solutions for

0=-0.13d^2+d+2

How you tackel it will depend on where you are with your maths. You could graph it (e.g. use Excel), guess values and slowly get closer to the answer or use the general equation to solve a quadratic.

For the latter:

d=-1+/-(1-4x-0.13x2)^0.5/(-0.13x2)

I get approximately 9.35 metres

but check my working.

mario teaches science workshops .he is presenting an activity on falling objects. when mario drops a ball, it bounces back up to two thirds of the height from which it was dropped. mario starts by dropping the ball from a height of 135cm. determine the height of the third bounce.

To find how far the ball travels horizontally before hitting the floor, we need to determine the value of d when the height h(d) is equal to zero. In other words, we want to find the horizontal distance at which the equation h(d) = -0.13d^2 + d + 2 equals zero.

To solve the equation -0.13d^2 + d + 2 = 0, you can use the quadratic formula, which is:

d = (-b ± sqrt(b^2 - 4ac)) / (2a)

In this equation, a = -0.13, b = 1, and c = 2. Plugging in these values into the quadratic formula, we have:

d = (-(1) ± sqrt((1)^2 - 4(-0.13)(2))) / (2(-0.13))

Simplifying further:

d = (-1 ± sqrt(1 + 1.04)) / (-0.26)

Now, we can calculate the value of d by plugging this into a calculator or using a computer algebra system. After evaluating the expression, we get two possible values for d: d ≈ 10.6 and d ≈ -5.7.

Since distance cannot be negative in this context, we can discard the negative value. Therefore, the ball travels approximately 10.6 meters horizontally before hitting the floor.