A projectile is projected in xy-plane with a speed of 10 m/s at an angle `theta` to the horizontal x-axis such that it passes through point (2,3). If two angles possible are `theta_(1)` and `theta_(2)`, find `tan theta_(1)-theta_(2)`.

Answer

6

Explanation

`y= tan theta-(1/2 gx^(2))/(u^(2) cos^(2) theta)`
`3=2 tan theta-1/2 xx(10xx4)/100(1+tan^(2) theta)`
`(tan^(2) theta)/5-2 tan theta +16/5=0`
`tan theta=(2pmsqrt(4-64/25))/(2//5) =(2 pm 6/5)/(2//5)=8.2`
`tan theta_(1)-tan theta_(2)=6`