h = 5 + 25t - 16t^2

Question

Jon is hitting baseballs. when he tosses the ball into the air, his hand is 5 feet above the ground, he hits the ball when it falls back to a height of 4 feet. the height of the ball is given by h = 5 + 25t - 16t^2, where t is in seconds. How much time will pass before jon hits the ball? what is the maximum height the ball attains?

Answer 1

To find out how much time passes before Jon hits the ball, set h=4.  This is the height he hits the ball when it falls.

 

4 = 5 + 25t - 16t²

 

 

Subtract 4 on both sides of the equation.

 

0 = 1 + 25t - 16t²

 

 

Solve for t using the quadratic formula:

 

t = (-b ± √(b² - 4ac)) / 2a

 

where:

a = -16

b = 25

c = 1

 

 

Accept the positive value of t.

 

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To find the maximum height of the ball, we find the vertex of the equation

 

h = 1 + 25t - 16t²

 

 

We use this equation because it represents the situation in which Jon hits the ball.

 

Use the axis of symmetry equation to find the x-coordinate of the vertex.

 

t = -b / (2a)

 

where:
a = -16

b = 25

 

 

Then evaluate h at that t value to find the y-coordinate of the vertex.