The range of a missile launched at 30 degrees is 240 m. If the missile is launched at the same speed but the angle at which it is launched is changed to 60 degrees the range of the missile has to be determined.
The range of a projectile launched at a velocity with magnitude v and at an angle x is given by R = v^2*sin 2x/g.
For a launch angle of 30 degrees, the range is 240 m. Substituting these values in the formula R = v^2*sin 2x/g
240 = v^2*sin 60/g ...(1)
Let the range of the missile when fired at the same speed but at an angle of 60 degrees be R.
R = v^2*sin 120/g ...(2)
Divide (2) by (1)
R/240 = v^2*sin 120/(v^2*sin 60)
=> R = 240*sin 120/sin 60 = 240
The range of the missile is equal if it is fired with the same speed and the angle it is fired at is changed from 30 degrees to 60 degrees.