Cliff diver jump from a height of 85 to 115 feet above the water. After t seconds the diver has fallen 16tto the 2nd power feet.
does the diver jumping from 85 feet reach the surface of the water within 2 seconds- why or why not.
85=16*t^2
t^2=85/16
t= sqrt (85/16) You do the math.
85
67 feet
To determine if the diver jumping from 85 feet reaches the surface of the water within 2 seconds, we need to compare the height fallen by the diver to the height above the water at any given time.
Given:
Initial height above water (h₀) = 85 feet
Final height above water (h) = 115 feet
Height fallen after t seconds (d) = 16t² feet
To solve the problem, we need to set up an equation based on the given information. We know that the total height fallen, d, is the difference between the initial height, h₀, and the final height, h, at any given time t:
d = h₀ - h
Substituting the given values into the equation:
16t² = 85 - 115
Simplifying the equation:
16t² = -30
We can see that this equation has no real solutions. When we solve the equation, we get a negative value under the square root, which is not possible here. This means that the height fallen by the diver, 16t², will never reach a value of -30 feet.
Therefore, the diver jumping from 85 feet does not reach the surface of the water within 2 seconds.