Problem 2-95 Linear Kinematics - Part 5

A camera is set up to take photographs of a ball undergoing vertical motion. The camera is \(5.2\; m\) above the ball launcher, which can launch the ball with an initial velocity of \(17\; m/s\) upward. Assuming that the ball goes straight up and straight down past the camera, at what times will the ball pass the camera?

Accumulated Solution

diagram of camera capturing a ball moving vertically

\(y = v_{0^t} + (1/2)at^2 \\ 5.1 = 17t - 4.9t^2 \\ y = \frac{-b}{2a} \pm \frac{\sqrt {b^2 - 4ac}}{2a}\)

\(t = \frac{3.47}{2} \pm \frac{\sqrt{12.041 -4.245}}{2} \\ = 1.735 \pm 1.396 \\ = 3.1\; s \; \text{or} \; 0.34 \; s\)

Which statement is correct?

(A)    In the solution of the quadratic equation, if both roots are real, only one has physical meaning.

(B)    In the solution of the quadratic equation, if both roots are real, they both have physical meaning.

(C)    In the solution of the quadratic equation, if both roots are real, only the positive values have physical meaning.