You're in an airplane that flies horizontally with speed 860 km/h (240 m/s ) when an engine falls off. Neglecting air resistance, assume it takes 26 s for the engine to hit the ground.
Hight of airplane is:
H = 3.3 km
horizontal distance that the aircraft engine falls:
d = 6.2 km
If the airplane somehow continues to fly as if nothing had happened, what is the distance between the engine and the airplane at the moment the engine hits the ground?
Express your answer to two significant figures and include the appropriate units.
Vo = 860km/h = 240 m/s. = Hor. speed.
d = Vo * T = 0. 240km/s * 26s = 6.2 km.
Well, it seems like the airplane is in quite an engine predicament! Let's do some calculations to figure out the distance between the engine and the airplane when the engine hits the ground.
First, we need to determine the time it takes for the engine to hit the ground. Given that it takes 26 seconds for the engine to fall, we know that the engine and the plane will be separated by time for that duration.
Now, let's find the distance the airplane travels in 26 seconds. Since the plane flies horizontally at a speed of 240 m/s, we can use the formula:
distance = speed × time
distance = 240 m/s × 26 s = 6240 m
So, the plane will have traveled a distance of 6240 meters in 26 seconds.
Now, let's look at the height of the airplane. We're given that it is 3.3 km high. To have a better understanding of the situation, let's convert the height to meters:
3.3 km × 1000 m/km = 3300 m
So, the height of the airplane is 3300 meters.
Finally, we can calculate the distance between the engine and the airplane at the moment the engine hits the ground. This can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
distance^2 = horizontal distance^2 + height^2
distance^2 = (6240 m)^2 + (3300 m)^2
distance^2 ≈ 38,976,000 m^2 + 10,890,000 m^2
distance^2 ≈ 49,866,000 m^2
distance ≈ √(49,866,000 m^2) ≈ 7060 m ≈ 7.1 km
So, the distance between the engine and the airplane at the moment the engine hits the ground is approximately 7.1 kilometers.
To solve this problem, we will first find the time it takes for the engine to hit the ground. Given that the height of the airplane (H) is 3.3 km and neglecting air resistance, we can use the formula:
t = sqrt((2H) / g)
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the values, we get:
t = sqrt((2 * 3300 m) / (9.8 m/s^2))
t = sqrt(6600 / 9.8)
t = sqrt(673.47)
t ≈ 25.97 s
So, the time it takes for the engine to hit the ground is approximately 25.97 s.
Now, we can find the distance between the engine and the airplane at the moment the engine hits the ground. Since the airplane is flying horizontally with a speed of 860 km/h, the horizontal distance covered by the airplane in 25.97 s is given by:
d_airplane = (860 km/h) * (25.97 s)
d_airplane = (860 km/h) * (25.97 s) * (1000 m/km) * (1 h/3600 s)
d_airplane ≈ 604.31 m
Therefore, the distance between the engine and the airplane at the moment the engine hits the ground is approximately 604.31 meters.
To find the distance between the engine and the airplane at the moment the engine hits the ground, we need to consider the horizontal velocity of the airplane and the time it takes for the engine to fall.
Given:
Horizontal velocity of the airplane: 240 m/s
Time for the engine to fall: 26 s
We know that the horizontal distance covered by an object in motion is given by the formula:
d = v * t
where:
d = distance covered
v = velocity
t = time
Using this formula, we can calculate the horizontal distance covered by the engine:
d = 240 m/s * 26 s
d ≈ 6240 m
So, the horizontal distance covered by the engine is approximately 6240 meters (or 6.24 km).
Now, to find the distance between the engine and the airplane, we need to subtract the horizontal distance covered by the engine from the initial horizontal distance between the engine and the airplane:
Distance between engine and airplane = Initial horizontal distance - Horizontal distance covered by the engine
Given:
Initial horizontal distance between engine and airplane: 6.2 km
Horizontal distance covered by the engine: 6.24 km
Distance between engine and airplane = 6.2 km - 6.24 km
Distance between engine and airplane ≈ -0.04 km
Since the distance between the engine and the airplane is negative, it means they are approximately at the same horizontal position at the moment the engine hits the ground.
Thus, the distance between the engine and the airplane at the moment the engine hits the ground is approximately -0.04 km (or -40 meters).
I gave the hor. distance. Maybe this is what they want:
d = sqrt(6.2^2 + 3.3^2) = 7.0 km.