Calculating Time and Distance of a Baseball's Horizontal Motion at 161 km/h

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A baseball is pitched horizontally at 161 km/h, covering a distance of 18.3 m to the batter. The time taken to travel the first half of the distance is calculated as 0.2 seconds, using the formula t = m/v. The second half of the distance also takes 0.2 seconds, assuming constant velocity. The ball's vertical drop under gravity during the first half can be calculated using the time of 0.2 seconds. The discussion emphasizes neglecting air resistance for these calculations.
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A baseball leaves a pitcher's hand horizontally at a speed of 161 km/h. The distance to the batter is 18.3 m. Neglect air resistance.

(a) How long does it take for the ball to travel the first half of that distance?

161*.27777=44.7m/s

t=m/v=(18.3/2)/44.7=.2 seconds

wrong...

(b) How long does it take for the ball to travel the second half of that distance?
should be the same as (a) right?
(c) How far does the ball fall under gravity during the first half?
can't do without time
(d) How far does the ball fall under gravity during the second half?
can't do without time
 
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0.2 s looks correct since the ball travels at constant velocity (neglecting air resistance).

Solve b with t = 0.2 s

and then solve c with the appropriate time 0.2 s later.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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