A tennis ball is thrown straight up into the air with an initial velocity of 6.8 m/s. How long does it take to reach the top of its trajectory?

To calculate the time it takes for a tennis ball to reach the top of its trajectory, we can use the following kinematic equation for an object under constant acceleration (which is gravity in this case):

v = u + at

Here, v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

At the top of the trajectory, the final velocity (v) of the tennis ball is 0 m/s because it comes to a momentary stop before starting to fall back down. The initial velocity (u) is given as 6.8 m/s. The acceleration (a) is due to gravity, which is approximately -9.8 m/s^2 on the surface of the Earth. The negative sign indicates that gravity is working in the opposite direction to the initial velocity.

Now, rearrange the equation to solve for time (t):

t = (v - u) / a

Plugging the given values into the equation:

t = (0 m/s - 6.8 m/s) / (-9.8 m/s^2)

t = (-6.8 m/s) / (-9.8 m/s^2)

t = 0.69387755102 seconds

Therefore, the tennis ball takes approximately 0.69 seconds to reach the top of its trajectory.