You're in an airplane that flies horizontally with speed 830km/h (230m/s ) when an engine falls off. Neglecting air resistance, assume it takes 35s for the engine to hit the ground.
Find the height of airplane.
Find the horizontal distance that the aircraft engine falls.
To find the height of the airplane, we can use the kinematic equation:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (which is approximately 9.8 m/s^2), and t is the time taken for the engine to hit the ground.
Substituting the given values:
h = (1/2) * 9.8 * (35^2)
h = 0.5 * 9.8 * 1225
h = 6025 m
Therefore, the height of the airplane is 6025 meters.
To find the horizontal distance that the aircraft engine falls, we can use the formula:
d = v * t
where d is the distance, v is the horizontal velocity of the aircraft (230 m/s), and t is the time it takes for the engine to hit the ground.
Substituting the given values:
d = 230 * 35
d = 8050 m
Therefore, the horizontal distance that the aircraft engine falls is 8050 meters.
To find the height of the airplane, we can use the formula for the free fall motion:
h = (1/2) * g * t^2
Where:
h is the height
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time it takes for the engine to hit the ground (35s)
Substituting the values into the formula, we get:
h = (1/2) * (9.8 m/s^2) * (35s)^2
h = 1/2 * 9.8 m/s^2 * 1225 s^2
h ≈ 6023.5 meters
So the height of the airplane is approximately 6023.5 meters.
To find the horizontal distance that the aircraft engine falls, we can use the formula for the horizontal distance:
d = horizontal velocity * time
Where:
d is the horizontal distance
horizontal velocity is the speed of the airplane (230 m/s)
time is the time it takes for the engine to hit the ground (35s)
Substituting the values into the formula, we get:
d = 230 m/s * 35s
d = 8050 meters
So the horizontal distance that the aircraft engine falls is 8050 meters.
t = time of free fall = 35 s
Horizontal distance
= horizontal speed × duration of free fall
For the vertical component of free fall,
Vyi=initial vertical velocity = 0
a=vertical acceleration = -g = -9.8 m/s²
ΔY = vertical position change
ΔY = Vyi(t)+(1/2)at²
Substitute numerical values to calculate required distances.