Diver jumps off a platform at an initial upward velocity of 20ft per second into the air above a pool The height of the diver above the water after jumping can be represented by the function h(t)=-16t^2 + 20t. Identify the x intercept and interpret its meaning

Question

(1.25,0) the horizontal distance of the length of the jump is 1.25
(0.625,6.25) the diver will reach a maximum height of 6.25 feet 0.625 seconds after he jumps
(1.25,0). The diver will enter the water 1.25 seconds after he jumps
(0,0) the diver jumps off the platform with an initial height of 0 feet

Answer 1

To find the x-intercept of the function \( h(t) = -16t^2 + 20t \), we set \( h(t) = 0 \):

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

Factoring out \( t \):

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

This gives two solutions:

1. \( t = 0 \)
2. \( -16t + 20 = 0 \)
   \[ -16t = -20 \]
   \[ t = \frac{20}{16} = 1.25 \]

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

Interpretation of the x-intercepts:

• At \( (0, 0) \): This point indicates that the diver jumps off the platform at time \( t = 0 \) seconds from an initial height of 0 feet.
• At \( (1.25, 0) \): This point indicates that the diver will enter the water 1.25 seconds after jumping off the platform.

Conclusion:

The correct interpretation of the x-intercept \( (1.25, 0) \) is:

(1.25, 0). The diver will enter the water 1.25 seconds after he jumps.