A ball thrown vertically into the air has its height above ground given by , where t is in seconds and s is in feet. Find the maximum height of the ball.
A) 242 feet
B) 121 feet
C) 8 feet
D) 16 feet
E) 229 feet

Question

A ball thrown vertically into the air has its height above ground given by  , where t is in seconds and s is in feet. Find the maximum height of the ball. ​
A) 242 feet 
B) 121 feet 
C) 8 feet 
D) 16 feet 
E) 229 feet

Quizplus · Accepted Answer

To find the maximum height of the ball, we need to find the vertex of the parabola given by the equation. The vertex is given by the point (t, s) where t is the time at which the ball reaches its maximum height and s is the maximum height. The equation is in the form of y = ax^2 + bx + c, and we can use the formula for the x-coordinate of the vertex, which is given by -b/2a. In this case, a = -16 and b = 96, so the time of the maximum height is t = -b/2a = -96/-32 = 3 seconds. We can plug t = 3 into the equation to find the maximum height:

s = -16(3)^2 + 96(3) + 8
s = -144 + 288 + 8
s = 152

Therefore, the maximum height of the ball is 152 feet, which corresponds to choice E.

A Ball Thrown Vertically into the Air Has Its Height