An airplane is flying horizontally at a velocity of 50.0 m/s at an altitude of 125 m. It drops a package to observers on the ground below. Approximately how far will the package travel in the horizontal direction from the point that it was dropped

To find out how far the package will travel horizontally from the point it was dropped, we need to determine the time it will take to reach the ground.

First, let's find the time it takes for the package to fall to the ground. We can use the equation for freefall:

h = (1/2)gt^2

Where:
h - height (125 m)
g - acceleration due to gravity (9.8 m/s^2)
t - time

Rearranging the equation, we have:

t^2 = (2h/g)

t = √(2h/g)
t = √(2 * 125 / 9.8)
t ≈ √25.51
t ≈ 5.05 s

Now that we have the time it takes for the package to fall, we can calculate the horizontal distance traveled:

distance = velocity * time
distance = 50.0 m/s * 5.05 s
distance ≈ 252.5 m

Therefore, the package will travel approximately 252.5 meters in the horizontal direction from the point it was dropped.

To determine the horizontal distance that the package will travel, we need to consider that the horizontal velocity of the airplane remains constant, assuming there are no external forces acting on it.

We can use the formula for horizontal distance (d) traveled by an object, which is given by the equation:

d = v * t,

where:
d = horizontal distance traveled
v = horizontal velocity of the object
t = time of flight.

In this case, the package is dropped from an airplane flying at a horizontal velocity of 50.0 m/s. Since the package starts with the same horizontal velocity as the airplane, it will continue to move with that velocity horizontally.

Now, to find the time of flight (t), we need to calculate the time it takes for the package to fall from an altitude of 125 m to the ground. We can use the formula for time (t) given by:

t = sqrt((2 * h) / g),

where:
h = initial vertical height or altitude
g = acceleration due to gravity (approximately 9.8 m/s^2 on the Earth's surface).

Plugging in the values, we get:

t = sqrt((2 * 125) / 9.8)
t = sqrt(250 / 9.8)
t ≈ sqrt(25.51)
t ≈ 5.05 s.

Since the package falls for approximately 5.05 seconds before it reaches the ground, we can now calculate the horizontal distance traveled using the equation:

d = v * t
d = 50.0 m/s * 5.05 s
d ≈ 252.5 m.

Therefore, the package will travel approximately 252.5 meters in the horizontal direction from the point it was dropped.

Without air resistance, time to drop to ground (irrespective of horizontal velocity)

t = √(2gh)

horizontal distance
= horiz. velocity * t

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