Question

A projectile is fired an angle of 45^o with the horizontal.Elevation angle of the projectile at the highest point as seen from the point of projection is

60^o

tan^-1(1/2)

$tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses$

45^o

Solution

tan^-1(1/2)

Height of projectile

straight H space equals space fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction straight H space equals space fraction numerator straight u squared sin squared 45 to the power of straight o over denominator 2 straight g end fraction straight H space equals space fraction numerator straight u squared over denominator 4 straight g end fraction Range space of space projectile straight R space equals space fraction numerator straight u squared sin space 2 straight theta over denominator straight g end fraction space equals fraction numerator straight u squared sin space 90 to the power of straight o over denominator straight g end fraction space straight R space equals space straight u squared over straight g straight R over 2 space equals space fraction numerator straight u squared over denominator 2 straight g end fraction tan space straight alpha space equals space fraction numerator straight H over denominator straight R divided by 2 end fraction space equals space fraction numerator straight u squared divided by 4 straight g over denominator straight u squared divided by 2 straight g end fraction tan space straight alpha space equals space 1 half straight alpha space equals space tan to the power of negative 1 end exponent space open parentheses begin inline style 1 half end style close parentheses

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