To solve this problem, we can use the equations of motion to determine the horizontal distance traveled by the object. Since the object is thrown horizontally, its initial vertical velocity is 0 m/s.
The key equation we can use is:
d = v * t
where: d is the horizontal distance traveled, v is the initial horizontal velocity (10 m/s in this case), and t is the time of flight.
To find the time of flight, we can use the equation for vertical motion:
y = (1/2) * g * t^2
where: y is the vertical displacement (50 m in this case), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time of flight.
Rearranging the equation for time of flight:
t = sqrt(2 * y / g)
Substituting the values:
t = sqrt(2 * 50 / 9.8) = sqrt(10.2) ≈ 3.19 s
Now, we can substitute the values of v and t into the equation for horizontal distance:
d = v * t = 10 * 3.19 ≈ 31.9 m
Therefore, the object will land approximately 31.9 meters from the base of the cliff.