An airplane is flying 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 flare is released from the plane. The flare hits the target on the ground. What is the angle è?
My goodness! Ten different physics questions were posted from the same person who used two different names.
Physics tutors are very busy here and usually only respond to posts in which the student has shown his/her efforts to answer the question.
no im not using two different names..
41.51 degrees
To find the angle è, we can break down the velocity of the airplane into horizontal and vertical components.
First, let's find the horizontal and vertical components of the airplane's velocity. The horizontal component is given by the equation:
Vx = V * cos(θ)
where Vx is the horizontal component of velocity, V is the magnitude of velocity (240 m/s), and θ is the angle (30.0°).
Vx = 240 * cos(30.0°)
Vx = 240 * 0.866
Vx ≈ 207.8 m/s
The vertical component is given by the equation:
Vy = V * sin(θ)
where Vy is the vertical component of velocity.
Vy = 240 * sin(30.0°)
Vy = 240 * 0.5
Vy = 120 m/s
Now, let's consider the motion of the flare. While the plane is flying, the horizontal component of the flare's velocity remains constant at 207.8 m/s. The vertical component of the flare's velocity, however, decreases due to gravity.
We can find the time it takes for the flare to hit the ground using the formula:
t = -(2 * Vy) / g
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time.
t = -(2 * 120) / 9.8
t = -240 / 9.8
t ≈ - 24.5 s
Since time cannot be negative, we discard the negative sign. So, it takes approximately 24.5 seconds for the flare to hit the ground.
Next, we can find the horizontal distance traveled by the flare during this time. The horizontal distance can be found using the equation:
dx = Vx * t
where dx is the horizontal distance.
dx = 207.8 * 24.5
dx ≈ 5081.1 m
The flare hits the target on the ground, which means that the horizontal distance traveled by the flare is equal to the initial horizontal distance of the airplane, which is 2.4 km or 2400 m.
Setting dx equal to 2400 m, we can solve for t to find the time it takes for the flare to hit the target:
2400 = 207.8 * t
t = 2400 / 207.8
t ≈ 11.6 s
Now, we have the time it takes for the flare to hit the target. Using this time, we can find the vertical distance traveled by the flare:
dy = Vy * t + 0.5 * g * t^2
where dy is the vertical distance.
dy = 120 * 11.6 + 0.5 * 9.8 * (11.6)^2
dy ≈ 694.6 m
Now, we have the vertical distance traveled by the flare, which is 694.6 m.
To find the angle è, we can use the tangent function:
tan(è) = dy / dx
tan(è) = 694.6 / 2400
tan(è) ≈ 0.2894
Taking the inverse tangent (arctan or tan^(-1)) of both sides, we can find the angle è:
è = arctan(0.2894)
è ≈ 16.5°
Therefore, the angle è is approximately 16.5°.