Question

After how many seconds does the ball attain maximum height based on the equation t = -16t^2 + 110t + 2?

a) 3.4375 seconds
b) 4.0625 seconds
c) 5.0 seconds
d) 6.5625 seconds

Answer 1

The ball attains maximum height after 3.4375 seconds according to the given quadratic equation, which corresponds to option (a). This time is found by calculating the vertex of the quadratic equation.

Step-by-step explanation:

To determine after how many seconds the ball attains maximum height based on the equation t = -16t2 + 110t + 2, we need to find the time at which the velocity of the ball is zero (the top of its trajectory). This can be done by finding the vertex of the quadratic equation which represents the position of the ball as a function of time. The general form of a quadratic equation is at2 + bt + c, and the time at which the vertex occurs (maximum height) is given by -b/(2a). Substituting the coefficients from the equation given into this formula, we get:

t = -b/(2a) = -110/(2 * -16) = 110/32 = 3.4375 seconds.

Thus, the correct answer is option (a) 3.4375 seconds. This is the time when the ball reaches its maximum height.