Mathematics, 24.03.2020 21:47 NeriyahY

Michael drops a ball out of a second-story window (20 ft). The formula h(t)=-16t^2+vot+h o gives the height of the ball in feet as a function of time in seconds.
What is vo in this scenario?
What is h o in this scenario?
When will the ball hit the ground? (Round to the nearest hundredth)

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Answer from: joshbee2014

Step-by-step explanation:

In your formula, the -16t-squared term is representative of the acceleration due to gravity in feet per second squared. The next term v0 is the initial upwards velocity and h0 is the initial height from which the object was either dropped or launched upwards (and then gravity takes over and pulls it back down as gravity does!). If Michael is dropping the ball, it is in free fall and because he dropped it as opposed to throwing it up into the air creating parabolic motion, there is no upwards velocity at all. In other words, v0 = 0. The height from which Michael dropped the ball is 20 feet, so h0 = 20 and our quadratic is

s(t)=-16t^2+20

where s(t) is the position of the ball after a certain amount of time.

If we are asked when the ball will hit the ground, we know that ON the ground, the height of the ball is 0, right? Sub in 0 for s(t) and solve for t, the time it takes the ball to hit the ground. This is also the same exact thing as "how long was the ball in the air?"

0=-16t^2+20 and, factoring out whatever we can (which is very little):

0=-4(4t^2-5)

By the Zero Product Property, either -4 = 0 (which OF COURSE IT DOESN'T!!) or

4t^2-5=0

Solving for t gives us

4t^2=5 and

$t^2=+/-\frac{5}{4}$ and

$t=+/-\frac{\sqrt{5} }{2}$ which simplifies in decimals to either -1.12 seconds or 1.12 seconds. We all know that time will never be negative, so the time it takes for the ball to hit the ground is 1.12 seconds.

Learn this stuff as best as you can because it is the foundation for derivatives in calculus and two-dimensional motion in physics!

Answer from: Quest

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

Answer from: Quest

i believe the answer is letter c) 8

step-by-step explanation:

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Michael drops a ball out of a second-story window (20 ft). The formula h(t)=-16t^2+vot+h o gives the...

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