To determine how long it takes for the ball to reach the ground, we can use the equation of motion in the vertical direction. Since the ball is thrown horizontally, its initial vertical velocity is zero (since there is no initial vertical velocity component). The acceleration due to gravity (g) will cause the ball to accelerate downward.
The equation of motion in the vertical direction is:
h = ut + (1/2)gt^2
Where: h = vertical displacement (in this case, the height of the cliff) u = initial vertical velocity (which is zero) t = time g = acceleration due to gravity (approximately 9.8 m/s^2)
Plugging in the values:
80 = 0 * t + (1/2) * 9.8 * t^2
Simplifying the equation:
80 = 4.9 * t^2
Dividing both sides by 4.9:
16.3265 = t^2
Taking the square root of both sides:
t = √16.3265
t ≈ 4.04 seconds
Therefore, it takes approximately 4.04 seconds for the ball to reach the ground when thrown horizontally with an initial speed of 10 m/s from an 80 m cliff.