Question

An airplane is fl ying with a velocity of 240 m/s at an angle of 30.0° with the horizontal, as the drawing shows. When the altitude of the plane is 2.4 km, a fl are is released from the plane. The fl are hits the target on the ground. What is the angle θ?

Answer 1

Answer:

$\theta=41.52^{\circ}$

Explanation:

Given that,

Velocity of the  airplane, v = 240 m/s

Angle with horizontal, $\theta=30^{\circ}$

The altitude of the plane is 2.4 km, d = 2400 m

Vertical speed of the airplane, $v_y=v\ sin\theta=240\ sin(30)=120\ m/s$

Horizontal speed of the airplane, $v_x=v\ cos\theta=240\ sin(30)=207.84\ m/s$

So, the equation of the projectile for the flare is given by :

$4.9t^2+120t-2400=0$

On solving the above equation, we get the value of t as:

t = 13.04 seconds

Horizontal distance travelled,

$d=v_x\times t$

$d=207.84\times 13.04$

d = 2710.23 m

Let $\theta$ is the angle with which it hits the target. So,

$tan\theta=\dfrac{2400}{2710.23}$

$\theta=41.52^{\circ}$

Hence, this is the required solution.