A projectile is thrown in the upward direction making an angle of `60^@` with the horizontal direction with a velocity of `150 ms^-1`. Then the time after which its inclination with the horizontal is `45^@` is

Options

A. 15 s
B. 10.98 s
C. 5.49 s
D. 2.745 s

Answer

B

Explanation

Initial velocity of projectile `u = 147 ms^(-1)`
Let after time t, the inclination of projectile with the horizontal be `45^@` and its velocity be v. In this situation
`v_(x) = v_(y) , " or " ucos 60^(@) = u sin 60^(@) - "gt"`
`:. 147 xx1/2 =147 xxsqrt3/2-9.8 xx t`
or `9.8 t =(147)xx1/2=147 xxsqrt3/2-9.8 xxt`
or `9.8 t = (147)/2(sqrt3-1)=147/2(1.732-1)=(147xx0.732)/2`
or `t = (147xx0.732)/(2xx9.8) = 5.49 s`