Writing in mathematics

Question

Describe the plan or steps to solving the problem below to help support your assertions:

a pinecone drops from a tree branch that is 20 feet above the ground. The function h = -16t^2 + 20 is used. If the height h of the pinecone is in feet after t seconds, at about what time does the pinecone hit the ground?

Answer 1

So for this equation, we will say that the ground level is zero feet. We are given the equation of h = -16t^2 + 20.

We solve this equation for t = time.

-16t^2 + 20 = 0 (subtract 20 from both sides)

-16t^2 = -20 (then divide both sides by -16)

t^2 = 20/16 (now take the square root of the top and bottom of the fraction)

t = sq root of 20/ sq rt. of 16

t = 2 rt 5/ 4 or rt 5/2. This would be plus and minus ordinarily, but we cannot have a negative time value.

Bonus: The real equation used for this type of problem is h(t) = -16t² - 64t + 120. You will find it used many times for word problems involving the height using quadratic equations! I hope that helps.

Answer 2

Please see video.

Answer 3

To find the time that the pinecone hits the ground, we need to find t such that h(t) = 0, which means t is a root of the given quadratic function. We must solve the equation:

-16t² + 20 = 0

Subtract both sides of the equation by 20 and divide by -16 to get:

t² = 20/16 = 5/4

Therefore:

t = sqrt(5)/2 (We omit the negative square root because we can't go backwards in time.)