To determine how far away the ball will land from the cliff, we need to calculate the horizontal distance traveled by the ball.
Given: Initial horizontal velocity (u_x) = 3.4 m/s Height of the cliff (h) = 19.6 m
The horizontal distance (R) can be determined using the equation:
R = u_x * t
Since there is no horizontal acceleration, the time of flight (t) for the ball will be the same as if it were in freefall from the given height.
Using the equation for freefall:
h = (1/2) * g * t^2
where g is the acceleration due to gravity.
Solving for t:
2h = g * t^2
t^2 = (2h) / g
t = sqrt((2h) / g)
Substituting the given values:
t = sqrt((2 * 19.6) / 9.8) = sqrt(39.2 / 9.8) = sqrt(4) = 2 s
Now, substituting the calculated time (t) back into the equation for horizontal distance (R):
R = u_x * t = 3.4 * 2 = 6.8 m
Therefore, the ball will land approximately 6.8 meters away from the cliff.