A diver jumps from a platform 25 meters above the surface of the water. The divers height in meters above the water is given by the equation h(t)= -4.9t^2 + 4.5t +25, where t is the time in seconds after the diver jumps

When does the diver reach a height of 12 meters during his decent?

What is the maximum height of the diver, and how long does it take the diver to reach that height?

When does the diver enter the water?

Question

A diver jumps from a platform 25 meters above the surface of the water. The divers height in meters above the water is given by the equation h(t)= -4.9t^2 + 4.5t +25, where t is the time in seconds after the diver jumps

When does the diver reach a height of 12 meters during his decent?

What is the maximum height of the diver, and how long does it take the diver to reach that height?

When does the diver enter the water?

jakfishman · Answer

@snowflake0531 @AZ one of you help idk

AZ · Answer

For part 1, plug in height of 12 and solve for the time

h(t) = -4.9t^2 + 4.5t + 25

12 = -4.9t^2 + 4.5t + 25

-4.9t^2 + 4.5t + 13 = 0

Solve it using the quadratic formula

$ x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} $

when the equation is $ ax^2 + bx + c = 0$

You'll get two values for t. Remember that time cannot be negative so your final answer is the positive value of t

AZ · Answer

For the second part, to find the maximum height of the diver

That would be the vertex of our graph h(t) = -4.9t^2 + 4.5t + 25

To find the time when you're at the maximum height, if our equation was 
$ ax^2 + bx + c = 0$

then, the x-value or t in our question is found by $\dfrac{-b}{2a}$

To find the y-value of the vertex or the maximum height in our question, you plug in that x-value you just got into the equation so essentially $ f\left(\dfrac{-b}{2a}\right)$

AZ · Answer

For the third part, to find out when the diver hits the water- recall that he's 25 feet above the water

He's going to hit the water when his height is 0 so set the initial equation to 0 and solve

h(t) = -4.9t^2 + 4.5t + 25

0 = -4.9t^2 + 4.5t + 25

solve it using the quadratic equation

AZ · Answer

alternatively, you can graph the equation and find all the answers off of the graph https://www.desmos.com/calculator/vqpxgzdj0t part 1) when y = 12, what is the positive x-value on the graph? That's the time when the height is 12 part 2) what is the y-value of the vertex? That's the maximum height part 3) what is positive x-value when y = 0? That's the time when the diver hits the water