Atennis ball machine serves a ball vertically into the air from a height of 2 feet, with an intial speed of 130 feet per second. what is the maximum height, in feet, the ball will attain? round to the nearest hundredth

For this case, the first thing to do is write the equation of moving the ball.
 We have then:
 h (t) = - 16t ^ 2 + 130t + 2
 Deriving we have:
 h '(t) = - 32t + 130
 We match zero:
 -32t + 130 = 0
 We cleared t:
 t = 130/32
 t = 4.0625 s
 We evaluate the value of t = 4.0625 s in the equation of motion:
 h (4.0625) = - 16 * (4.0625) ^ 2 + 130 * (4.0625) + 2
 h (4.0625) = 266.0625 feet
 
 The maximum height, in feet, the ball will attain is:
 h (4.0625) = 266.0625 feet

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