Question

a tennis 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

Answer 1

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
 Answer:
 The maximum height, in feet, the ball will attain is:
 h (4.0625) = 266.0625 feet