an object falls directly from a plane flying horizontally at an altitude of 10000ft at 50mi/h. how long will it take to hit the ground?
It is a question which requires an unreasonable assumption, namely ignore air-resistance.
Without air-resistance, time it takes to reach ground is
t=sqrt(2H/g)
=sqrt(2*10000/32.2)
=24.9 s
The horizontal velocity of the plane does not change the time required.
If the dimensions and shape of the object is known, we can calculate the terminal velocity and the answer would be different.
t=sqrt(2H/g)
=sqrt(2*10000/32.2)
=24.9 s
To find the time it takes for the object to hit the ground, we need to consider the motion in the vertical direction. Since the object is falling vertically, we ignore the horizontal motion.
We can use the equation of motion for free fall:
h = ut + (1/2)gt^2
where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time.
Given:
Initial height (h) = 10000 ft
Acceleration due to gravity (g) = 32.2 ft/s^2 (approximate value)
Initial velocity (u) = 0 ft/s (since the object is dropped, not given initial horizontal velocity)
Substituting the values into the equation, we have:
10000 = 0 * t + (1/2) * 32.2 * t^2
Simplifying the equation, we get:
10000 = 16.1 * t^2
Dividing both sides by 16.1, we have:
t^2 = 10000 / 16.1
t^2 = 621.12
Taking the square root of both sides, we get:
t ≈ 24.91 seconds
Therefore, it will take approximately 24.91 seconds for the object to hit the ground.
To determine how long it will take for an object to hit the ground when falling from a plane, we can use basic kinematic equations. In this scenario, the object is falling vertically while the plane is moving horizontally.
To start, let's convert the units for altitude and velocity to a consistent system. We'll use feet and miles per hour (mi/h) for this explanation.
Given:
Altitude (h) = 10000 ft
Velocity (v) = 50 mi/h
We need to find the time (t) it takes for the object to fall to the ground.
The first step is to understand that horizontally flying at a constant velocity does not affect the vertical motion of an object (as long as air resistance is negligible). Therefore, we can treat the vertical motion of the object independently.
The equation that relates the distance fallen (d), the initial velocity (u), time (t), and acceleration due to gravity (g) is:
d = ut + (1/2)gt^2
In this case, the initial velocity (u) is zero because the object starts from rest. We can also assume that the only force acting on the object is gravity, resulting in an acceleration due to gravity (g) of approximately 32.2 ft/s^2.
Now, let's substitute the given values into the equation:
10000 = 0 + (1/2)(32.2)t^2
10000 = 16.1t^2
t^2 = 10000 / 16.1
t^2 ≈ 621.12
To solve for t, we take the square root of both sides:
t ≈ √(621.12)
t ≈ 24.92 seconds
So, it will take approximately 24.92 seconds for the object to hit the ground.