A diver jumps off a platform at an untoward velocity of 20 feet per second into the air above the pool. The height of the diver above the water after jumping can be represented by the function h(t) = -16t^2 + 20t what is the x intercept and interprets meaning

Answer 1

To find the x-intercept of the function \( h(t) = -16t^2 + 20t \), we need to set \( h(t) \) equal to zero and solve for \( t \):

\[ -16t^2 + 20t = 0 \]

We can factor out \( t \) from the equation:

\[ t(-16t + 20) = 0 \]

This gives us two solutions:

1. \( t = 0 \) (the time when the diver just jumped off the platform)
2. \( -16t + 20 = 0 \)

Now solve for \( t \) in the second part:

\[ -16t + 20 = 0 \]

\[ -16t = -20 \]

\[ t = \frac{20}{16} = \frac{5}{4} = 1.25 \text{ seconds} \]

Thus, the x-intercepts are \( t = 0 \) and \( t = 1.25 \).

Interpretation of Meaning:

The x-intercepts represent the times at which the height of the diver \( h(t) \) is 0, meaning the diver is at the water's surface.

• At \( t = 0 \) seconds, the diver is just about to jump from the platform.
• At \( t = 1.25 \) seconds, the diver hits the water after jumping off the platform.

In summary, the diver enters the water again after 1.25 seconds.