Question

A basket ball is at the top of a hill that is 23 feet tall. After 2.5 second the basketball is 18 feel above the ground. Find a value, write in vertex form, how long it will take to reach the ground, how far is it off the ground in 3 seconds?

Answer 1

f(x) = -ax² + 23

f(2.5) = -6.25a + 23 = 18

-6.25a = -5

a = 4/5

f(x) = (-4/5)x² + 23

f(3) = (-4/5)(3²) + 23 = 15.8 feet

Answer 2

The question involves solving a projectile motion problem in mathematics using the principles of physics to determine when a basketball will reach the ground and its height at different times.

Step-by-step explanation:

The subject of this question is Mathematics, specifically involving free-fall and projectile motion under the influence of gravity. Given the initial conditions of a basketball's height above the ground and its position after a certain time, we are asked to find a value in vertex form, the time it will take for the ball to reach the ground, and the ball's height above the ground after 3 seconds.

Using the laws of physics and the standard formula for the motion of an object under gravity (ignoring air resistance), the position of the ball y(t) at time t can be given by the quadratic equation y(t) = h - (1/2)gt^2, where h is the initial height, and g is the acceleration due to gravity (approximately 9.8 m/s^2 or 32 ft/s^2). The vertex form of this parabolic motion will be in the shape of y(t) = a(t - h)^2 + k. The problem can be solved by applying these motions and using corresponding values to calculate the time it takes for the basketball to hit the ground.