Question
Wed April 22, 2015 By: Navya Benny

Sir/Madam
 
This question is also not from this chapter but from the previous year.
 
The ceiling of a long hall is 25m high. What is the maximum horizontal distance that a ball thrown with a speed of 40m/s can go without hitting the ceiling of the ball?

Expert Reply
Jyothi Nair
Thu April 23, 2015
Given that the maximum height = 25 m
Velocity with which the ball is thrown, u = 40 m/s
Horizontal range = ?
begin mathsize 12px style We space know space that space maximum space height comma space straight h subscript max space equals space fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction 2 cross times straight h subscript max cross times straight g space equals space straight u squared sin squared straight theta sin squared space straight theta space equals space fraction numerator 2 cross times straight h subscript max cross times straight g over denominator straight u squared end fraction sin squared space straight theta space equals fraction numerator 2 cross times 25 cross times 9.8 over denominator open parentheses 40 close parentheses squared end fraction sin squared space straight theta equals 0.30625 sin space straight theta space equals 0.5534 straight theta space equals space sin to the power of negative 1 end exponent open parentheses 0.5534 close parentheses straight theta space equals space 33.6 degree Horizontal space range space is space given space by colon space fraction numerator straight u squared sin space 2 straight theta over denominator straight g end fraction Maximum space horizontal space distance space equals space fraction numerator open parentheses 40 close parentheses squared space sin space open parentheses 2 cross times 33.6 degree close parentheses over denominator 9.8 end fraction space equals space 150.5 space straight m   end style
The maximum horizontal distance the ball will reach = 150.5 m 
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