An airplane is flying with a velocity of 248 m/s at an angle of 30.0° with the horizontal, as the drawing shows. When the altitude of the plane is 2.8 km, a flare is released from the plane. The flare hits the target on the ground. What is the angle?

What angle? The angle of the flare tyrajectory with respect to the ground when it hits?

That would be arctan(Vy/Vx)

I assumw you know how to calsulate Vy and Vx at impact.

Vy will be negative; so will the angle

To find the angle at which the flare hits the target on the ground, we can break down the velocity of the airplane into its horizontal and vertical components.

1. Horizontal Component:
The horizontal component of the velocity can be found using the formula:
Vx = V * cosθ
where Vx is the horizontal component of the velocity, V is the magnitude of the velocity (248 m/s), and θ is the angle with the horizontal (30.0°).

Vx = 248 m/s * cos(30.0°)
Vx = 248 m/s * 0.866
Vx = 214.67 m/s

2. Vertical Component:
The vertical component of the velocity can be found using the formula:
Vy = V * sinθ
where Vy is the vertical component of the velocity, V is the magnitude of the velocity (248 m/s), and θ is the angle with the horizontal (30.0°).

Vy = 248 m/s * sin(30.0°)
Vy = 248 m/s * 0.5
Vy = 124 m/s

3. Time of Flight:
To find the time of flight, we need to determine how long the flare is in the air. Since the flare is only affected by gravity in the vertical direction, we can use the vertical component of the velocity.

Vertical distance covered by the flare (altitude) = 2.8 km = 2800 m

Using the formula:
altitude = (Vy * t) + (0.5 * g * t^2)
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time of flight.

2800 m = (124 m/s * t) + (0.5 * 9.8 m/s^2 * t^2)

This is a quadratic equation in terms of t. Solve this equation to find the time of flight.

4. Angle at which the flare hits the ground:
Once we have the time of flight, we can find the angle at which the flare hits the ground using the horizontal component of the velocity.

Using the formula:
tanθ = (Vy - (g * t)) / Vx

Substitute the values we have calculated to find the angle.

Note: The result you obtain may need to be adjusted to ensure it is within the appropriate range (between 0° and 90°) for the given situation.