In order to demonstrate two dimensional motion, Dr. O\'Brien has employed the he

Question

In order to demonstrate two dimensional motion, Dr. O'Brien has employed the
help of one of his former students, lets call him "`Nirav the great"'. Dr. O'Brien
begins running across the quad starting from the base of Beatty hall, at a brisk
pace of 3m/s. Nirav the great is standing in a window of Beatty hall (at a height of
60m) directly above Dr. O'Brien (who is about 2m tall), and res water balloon at
Dr. O'Brien from a launcher that is aimed DIRECTLY HORIZONTAL. Students
on the ground below measure that the balloon hit Dr. O'Brien right in the back of
the head. It is noted that Nirav waited 4 seconds to re the water balloon after Dr.
O'Brien left his starting position. If this is the case, and the water balloon strikes
Dr. O'Brien, what was the initial velocity of the water balloon?

Explanation / Answer

vertically ballon have to travel 62 m with no initial vertical velocity.

using h = ut + at^2/2

-62 = 0 - 9.81t^2 /2

t = 3.56 sec

and it was launched after 4 sec .

so for 4 + 3.56 = 7.56s O]brien run .

horiontal distance travel O'brien and ballon = 7.56 x 3 = 22.67 m

so initial horizontal velocity of ballon = hori. distance traveled by ballon / time taken by ballon to reach ground

v = 22.67 / 3.56 =6.37 m/s

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