Calculating Time & Speed of Package Dropped from Plane

In summary, the airplane is traveling horizontally at a constant speed of 260 mph at an altitude of 500m. After ejecting a package with an initial velocity of 260 mph, it takes approximately 10.1 seconds for the package to reach sea level. The speed of the package when it hits the ground is the magnitude of the vector combining the horizontal and vertical velocities, with the vertical velocity being found by assuming it starts at zero and accelerates downward under gravity.
  • #1
Idealism_Theory
12
0

Homework Statement


airplane files horizontally with constant speed of 260 mph at an altitude of 500m. Ignore height of this point above sea level. Assume acceleration due to gravity is g= 9.8m/s^2

After ejecting a package from the plane, how long will it take for it to reach sea level from time it is ejected? Assume package has an initial velocity of 260mph in the horizontal direction. What is the speed of the package when it hits the ground (mph)?


Homework Equations



x = u t+ (1/2) a t^2
sqrt vx^2 + vy^2 (I don't know how to incorporate that into finding the speed though)
v=voy+ay(t)

The Attempt at a Solution




I've already found it will take 10.1s for the package to hit the ground and the horizontal distance it should be released from the plane is 1170m...but I'm not sure about finding vy. Please help. Thanks in advance.
 
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  • #2
One has to find the horizontal velocity vx and the vertical velocity vy, and add the two vectors.

v = [tex]\sqrt{v_x^2\,+\,v_y^2}[/tex]
 
  • #3
But I don't know vy!
 
  • #4
it appears that v_y was initially zero, for there was only horizontal velocity of 260mph... so simply v_y = u_y + a t and the speed you are after is probably the magnitude of your vector (need to combine the x and y components)
 
  • #5
Idealism_Theory said:
But I don't know vy!
As mjsd indicated, assume that the package is dropped with zero vertical velocity, then accelerates downward under the influence of gravity.

One was able to find the time at which the package struck the ground. One should be able to find the vertical velocity after falling 500 m with an acceleration of g.
 

What is the formula for calculating the time and speed of a package dropped from a plane?

The formula for calculating the time and speed of a package dropped from a plane is t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the gravitational acceleration (9.8 m/s²).

What units should be used for calculating time and speed of a package dropped from a plane?

The units that should be used for calculating time and speed of a package dropped from a plane are meters for distance, seconds for time, and meters per second (m/s) for speed.

How does air resistance affect the calculations for time and speed of a package dropped from a plane?

Air resistance can affect the calculations for time and speed of a package dropped from a plane by slowing down the descent of the package. This means that the package may take longer to fall and will have a lower speed than what is calculated using the formula.

What other factors should be considered when calculating the time and speed of a package dropped from a plane?

Other factors that should be considered when calculating the time and speed of a package dropped from a plane include the initial velocity of the package when it is dropped, the angle at which the package is dropped, and any external forces acting on the package during its descent.

What are some real-life applications of calculating the time and speed of a package dropped from a plane?

One real-life application of calculating the time and speed of a package dropped from a plane is in the delivery of packages by drones. By accurately calculating the time and speed of a package dropped from a drone, delivery companies can ensure that the package is delivered to the correct location and within a specific timeframe. Another application is in skydiving, where calculating the time and speed of descent is important for safety and precision in landing.

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