Answer:
The distance is [tex]d = 112.5 \ m[/tex]
Explanation:
From the question we are told that
The horizontal speed is [tex]v_x = 30 \ m/s[/tex]
The height is [tex]s = 69 \ m[/tex]
Generally from kinematic equation we have that
[tex]s = ut + \frac{1}{2} gt^2[/tex]
Here u is the initial velocity of the turd in the vertical direction and the value is 0 m/s
So
[tex]69 = 0 * t + \frac{1}{2} * 9.8 t^2[/tex]
=> [tex]t = \sqrt{\frac{2 * 69}{4.9} }[/tex]
=> [tex]t = 3.75 \ s[/tex]
Generally the distance which the robot have to hood the bucket in order to catch the turd is mathematically represented as
[tex]d = v_x * t[/tex]
=> [tex]d = 30 * 3.75[/tex]
=> [tex]d = 112.5 \ m[/tex]
