How many times does the soda cross the 10 foot threshold?

Question

You’ve been asked to build a machine for a TV commercial that launches soda bottles from ground level over a volleyball net. you estimate the soda needs to clear at least 10 feet in order to sail over the net. The equation that represents the height of the bottle as a function of time (t) in seconds is:

h=-16t^2+35.2t

Answer 1

You can work this out 2 ways.

From your equation, h= -16t² + 35.2t you can find the highest point the soda will reach once it is launched.

To find the vertex (x, y) of the parabolic path, let's first find the x-coordinate.

x = -b/2a (should sound familiar)

x = -35.2 / (2)(-16)

x = -35.2 / -32

x = 1.1

The x-coordinate represents time. In 1.1 seconds, the soda will reach its highest point.

To find that point, substitute the 1.1 for the t in your equation.

h = -16(1.1)² + 35.2(1.1)

h = 19.36 (this is the y coordinate of your vertex)

vertex = (1.1, 19.36)

So, in 1,1 seconds, the soda will reach a height of 19,36 feet.

This means that the soda will cross the threshold 2 times, once on the way up and once on the way down.

You can also solve the equation to find out when the soda will reach a height of 10 feet.

10 = -16t² + 35.2t

0 = -16t² + 35.2t -10

To solve for t, you will have to use the quadratic formula.

I won't write all of that out, but your answers will be

t = 1.865 or t = .335

This means in .335 seconds the soda will reach a height of 10 feet and again on its way back down in 1.865 seconds it will be at a height of 10 feet.

You need to use which ever procedure is easier and makes more sense to you.

That is unless, of course, your teacher wants you to work this out a particular way.

Answer 2

10 < -16t^2+35.2t

Can you solve for t and answer?