Question

The height h, in feet, of an acorn that falls from a branch 100 ft above the ground depends on the time t, in seconds, since it has fallen. This is represented by the rule h = 100 - 16t^2. How can you determine how much time has elapsed when the acorn hits the ground algebraically?

Answer 1

To find the time when the acorn hits the ground, we set the equation h = 100 - 16t^2 to 0, solve the quadratic equation for t, and find that it takes 2.5 seconds for the acorn to reach the ground.

Step-by-step explanation:

To determine algebraically the time that has elapsed when the acorn hits the ground, you first need to set the equation h = 100 - 16t^2 equal to zero since the height h will be 0 when it hits the ground. Hence:

• 0 = 100 - 16t^2

You then solve for t. Since this is a quadratic equation in the form of at^2 + bt + c = 0, it can be reorganized to:

• 16t^2 = 100

Divide both sides by 16:

• t^2 = 100 / 16
• t^2 = 6.25

Take the square root of both sides:

• t = √6.25
• t = 2.5 seconds

The positive value of t is taken since time cannot be negative. Thus, it will take 2.5 seconds for the acorn to hit the ground after it is dropped.

Answer 2

Step-by-step explanation:

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