Problema Solution
A golf ball is hit with an initial velocity of 130 feet per second at an inclination
of 45◦ to the horizontal. In physics, it is established that the height h of the golf ball is given
by the function
h(x) = −(32/130^2)x^2 + x
where x is the horizontal distance that the golf ball has traveled.
1) What is the height of the golf ball after it has traveled 300 feet?
2)How far was the golf ball hit?
3)What was the maximum height of the ball?
Answer provided by our tutors
1) What is the height of the golf ball after it has traveled 300 feet?
x = 300 ft
h(300) = −(32/130^2)*300^2 + 300
h(300) = 129.59 ft
click here to see the step by step calculation
the height of the golf ball after it has traveled 300 feet is 129.59 feet.
2)How far was the golf ball hit?
we need to find x max that is for which value of x and x<>0 the height h(x) = 0
we will do that by solving the quadratic equation and finding the non-negative roots
−(32/130^2)x^2 + x = 0
x = 528.125 ft
click here to see the step by step solution of the quadratic equation
the golf ball was hit 528.125 feet far.
3)What was the maximum height of the ball?
we need to find the maximum of the parabolic function h(x) = −(32/130^2)x^2 + x
h max = c - b^2/4a where a = −(32/130^2), b = 1 and c = 0
h max = - 1^2/(4*(−(32/130^2))
h max = 132.03 ft
click here to see the graph of the function
the maximum height of the ball is 132.03 feet.