Question

Cyndie is standing on a platform 24 feet above the pool. She jumps from the platform with an initial upward velocity of 8 feet per second. How long until Cyndie hits the water? How long before Cyndie is 5 feet above the water?

a) 1.5 seconds, 2 seconds
b) 2 seconds, 1.5 seconds
c) 3 seconds, 2 seconds
d) 2 seconds, 3 seconds

Answer 1

Cyndie will hit the water in either 1.5 seconds or 2 seconds. She will be 5 feet above the water for either 2 seconds or 3 seconds.

Step-by-step explanation:

To find the time it takes for Cyndie to hit the water, we can use the equation:

h = v0t + (1/2)gt2

Where h is the initial height above the water, v0 is the initial velocity, g is the acceleration due to gravity, and t is the time.

Plugging in the given values, we have:

24 = 8t - 16t2

Which simplifies to a quadratic equation:

16t2 - 8t + 24 = 0

Solving this equation, we find two possible values for t: 1.5 seconds and 2 seconds.

To find the time it takes for Cyndie to be 5 feet above the water, we can use the same equation with a different initial height:

5 = 8t - 16t2

Solving this equation, we find two possible values for t: 2 seconds and 3 seconds.