Question

On Mars, if you hit a baseball, the height of the ball at time t would be modeled by the quadratic function h(t) = -1.85t² + 20t + 1. When will the ball hit the ground?

a) t = 1.35 seconds
b) t = 2.85 seconds
c) t = 4.20 seconds
d) t = 5.60 seconds

Answer 1

The ball will hit the ground at t = 1.35 seconds.

Step-by-step explanation:

The ball will hit the ground when its height is 0. To find the time it takes for the ball to hit the ground, we need to find the value of t when h(t) = 0. We can do this by setting the quadratic function h(t) = -1.85t² + 20t + 1 equal to 0 and solving for t using the quadratic formula.

1. Plug in the values of a = -1.85, b = 20, and c = 1 into the quadratic formula: t = (-b ± √(b² - 4ac))/(2a)
2. Calculate the discriminant, which is the expression inside the square root: b² - 4ac
3. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions.
4. In this case, the discriminant is positive, so there are two real solutions: t = 1.35 seconds and t = 2.85 seconds
5. Since we're only interested in the time when the ball hits the ground, we choose the smaller positive solution, which is t = 1.35 seconds.