Question

Two balls are thrown from the same point at same time,one vertically upwards with speed of 25meters per second and the other vertically downwards with a speed of 15meters per second.Find how far apart the balls are after 5 seconds and the velocities of the balls?

Answer 1

$$v _ {1} = 25 \, \text{m/s}, \, v _ {2} = -15 \, \text{m/s}, \, T = 5 \, \text{s}.$$

The coordinates of the first ball and the second balls after $t$ seconds are

$$y _ {1} (t) = v _ {1} t - \frac {g t ^ {2}}{2},$$ $$y _ {2} (t) = v _ {2} t - \frac {g t ^ {2}}{2},$$

respectively, where $g = 9.8 \, \text{m/s}^2$ is the acceleration of gravity and the positive direction of the Y axis is upward. The distance between the balls after $t = T$ is

$$S = \left| y _ {1} (T) - y _ {2} (T) \right| = \left(v _ {1} - v _ {2}\right) T = 200 \, \text{m}.$$

The velocities of the balls are

$$u _ {1} = v _ {1} - g T = - 24 \, \frac{\text{m}}{\text{s}},$$ $$u _ {2} = v _ {2} - g T = - 24 \, \frac{\text{m}}{\text{s}},$$

The sign "minus" means that the both velocities are directed downward.