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Chapter 0: Problem 59

Write an original word problem that can be solved using a quadratic equation. Then solve the problem.

Short Answer

Expert verified
The volleyball player hits the ball at t=1 second.

Step by step solution

01

Write an Original Problem

A volleyball player hits a ball when its 1 m above the ground. The height, \(h\), in meters, of the volleyball can be represented by \(h(t) = -5(t - 2)^2 + 5\), where \( t\) is the time in seconds since the ball has been hit.
02

Formulate the Quadratic Equation

The goal is to find out when will the ball hit the ground, i.e., when \(h(t)=0\). So the equation becomes \(0 = -5(t - 2)^2 + 5\)
03

Solve the Quadratic Equation

Step 1: Multiply both sides by -1 to simplify and then add 5 to both sides: \(5= 5(t - 2)^2\) \n\n Step 2: Isolate the term with \(t\) by dividing both sides by 5: \(1= (t - 2)^2\)Step 3: Take the square root on both sides: \(卤\sqrt{1} =t - 2\)Step 4: Solve for \(t\): \( t = 2 卤 1\)That means the volleyball will hit the ground after 1 second \( (t = 2 - 1)\) or 3 seconds \( (t = 2 + 1)\) since it hits. But the solution \( t = 3\) seconds doesn't make sense in this case, because the ball can't hit the ground after it hits. So, we discard \( t = 3\) seconds.

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