A tennis ball is struck at a speed of 6 m/s horizontally, it departs from the racket at a vertical distance of a 1.02m. How much time is needed for the Ball to hit the ground?

how long does it take to fall 1.02m?

4.9t^2 = 1.02

the horizontal speed does not matter.

To find the time it takes for the tennis ball to hit the ground, we need to analyze the vertical motion of the ball.

First, we can use the equation of motion: s = ut + 0.5 * g * t^2.

Here:
s: vertical displacement = -1.02m (negative because the ball is moving downwards)
u: initial vertical velocity = 0 (since the ball is just released, so no initial velocity)
g: acceleration due to gravity = -9.8m/s^2 (negative because gravity acts in the downward direction)
t: time (to be determined)

Plugging in the values, we get:
-1.02 = 0 * t + 0.5 * (-9.8) * t^2

Simplifying the equation, we have:
-1.02 = -4.9 * t^2

Rearranging the equation, we get:
t^2 = 1.02 / 4.9

Taking the square root of both sides, we find:
t ≈ √(1.02 / 4.9)

Calculating the value, we have:
t ≈ √0.2082

Therefore, the approximate time needed for the tennis ball to hit the ground is around 0.456 seconds.