Problema Solution
a baseball player hits a pop up. The path of the ball can be modeled by y = -.105x2 + 4.2x + 3, where x is the distance in feet and y is the height in feet of the baseball. how high did the baseball go at its highest point. How long did it take to reach the highest point. How long did it take to the hit the ground
Answer provided by our tutors
We need to find the vertex for the parabolic function:
y = -0.105x^2 + 4.2x + 3
y max = c - (b^2/4a), where a = -0.105, b = 4.2, c = 3
y max = 3 - (4.2^2/(4*(-0.105))
y max = 45 ft
x max = -b/2a
x max = -4.2/(2*(-0.105))
x max = 20 s
The baseball went to 45 feet maximum height.
It needed 20 seconds to reach the highest point.
The ball will hit the ground after x seconds when y = 0 that is:
-0.105x^2 + 4.2x + 3 = 0
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click here to see the equation solved for x
........
x = 40.7 s
After 40.7 seconds the ball will hit the ground.