1.3 A student at Rice University has just returned from a Club 13 run. At this m

Question

1.3

A student at Rice University has just returned from a Club 13 run. At this moment, she realizes that a sneaky group of students has already dropped five buckets of water directly above her. She has no idea what floor of the dormitory the students were on, because they've already hidden themselves again behind the short wall of their balcony. However, she knows with certainty that she will lose all of her shaving cream if she doesn't react quickly. Given: the acceleration due to gravity is a = -g and the falling water has speed v0 and height h above her head at the instant she notices it. Show that if the student is to retain her modesty she must react in less time than

Explanation / Answer

initial velocity is v0

let final velocity be v

we know,

v02-v2=-2gh

=> v=(v02 +2gh)^0.5..............(i)

now , also

v=v0 +gt

=> t=1/g(-v0+v)........(ii)

putting (i) in (ii) we get

t=1/g(-v0 +(v02 +2gh)^0.5)

hence proved

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