Answer :
Answer:
[tex]\theta=41.52^{\circ}[/tex]
Explanation:
Given that,
Velocity of the airplane, v = 240 m/s
Angle with horizontal, [tex]\theta=30^{\circ}[/tex]
The altitude of the plane is 2.4 km, d = 2400 m
Vertical speed of the airplane, [tex]v_y=v\ sin\theta=240\ sin(30)=120\ m/s[/tex]
Horizontal speed of the airplane, [tex]v_x=v\ cos\theta=240\ sin(30)=207.84\ m/s[/tex]
So, the equation of the projectile for the flare is given by :
[tex]4.9t^2+120t-2400=0[/tex]
On solving the above equation, we get the value of t as:
t = 13.04 seconds
Horizontal distance travelled,
[tex]d=v_x\times t[/tex]
[tex]d=207.84\times 13.04[/tex]
d = 2710.23 m
Let [tex]\theta[/tex] is the angle with which it hits the target. So,
[tex]tan\theta=\dfrac{2400}{2710.23}[/tex]
[tex]\theta=41.52^{\circ}[/tex]
Hence, this is the required solution.