Question

Ana was given the following problem for homework to analyze:

Suppose a volleyball player serves from 1 behind the back line. If no other player touches the ball, it will land in bounds. The equation

ℎ()= −4.92 + 3.28 +1.7 gives the ball’s height, ℎ, in meters in terms of time, , in seconds.



Part A: Finally, Ana states that the ball will hit the ground after 1.012 seconds. Is she correct? Justify your answer.

Answer 1

Explanation:

The variable t is missing in the given equation as it should read:

ℎ(t)= −4.92t^2 + 3.28t + 1.7

When the ball will hit the ground, h=0

−4.92t^2 + 3.28t + 1.7 = 0

Using the quadratic formula to find the solution,

t = -0.34 or 1.01

As time cannot be negative, h=0 when t=1.01s. So Ana is correct.

Answer 2

The answer is very close, within the margin of error.

Explanation:

When the ball hits the ground, h(t) will equal 0

0 = −4.92t^2 + 3.28t +1.7

Using the quadratic equation

-b ± sqrt(b^2 -4ac)

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2a

where a = -4.92 b = 3.28 and c = 1.7

-3.28 ± sqrt(3.28^2 -4(-4.92)1.7)

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2(-4.92)

t≈-0.342418

t≈1.00908

The answer is very close, within the margin of error.