Question

H(t) = -16t² + 20t + 1.5 what is the coordinate point when the ball hits the ground?

a) (1.5, 0)

b) (0, 1.5)

c) (1, -16)

d) (20, 0)

Answer 1

We find when the ball hits the ground by solving the quadratic equation h(t) = -16t² + 20t + 1.5 for when h(t) = 0, using the quadratic formula. The positive root gives us the time at which the ball hits the ground, leading to the coordinate point (1.25, 0).

Step-by-step explanation:

To determine when the ball hits the ground using the given quadratic equation h(t) = -16t² + 20t + 1.5, we need to find the value of t for which the height h(t) is equal to 0. This is because the height above the ground is 0 when the ball hits the ground. Thus, we set the equation to 0 and solve for t:

0 = -16t² + 20t + 1.5

We can solve this quadratic equation using the quadratic formula:

t = √(∛2 - 4ac) / (2a)

Where:

• a = -16
• b = 20
• c = 1.5

The positive root of this equation will be the time when the ball hits the ground. We discard the negative root since it doesn't make physical sense in the context of the trajectory of a ball after it is released (time cannot be negative). Once we have the value of t, we have the coordinate point as (t, 0). Based on the solution of the quadratic equation, the time when the ball hits the ground is at t = 1.25 seconds (after applying the quadratic formula and choosing the positive root). Thus, the coordinate point when the ball hits the ground is (1.25, 0).