When Does the Package Reach the Ground?

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In summary, a helicopter is moving upwards at a speed of 5.5m/s and a package is dropped from a window at a height of 100m. Using the equation delta y = Vot + 1/2at^2, with Vo = 5.5m/s, a = -9.8m/s^2, and delta y = -100m, the time it takes for the package to reach the ground can be solved using the quadratic formula. The two solutions obtained using the formula are t = 5.11s and t = -10.46s, with only t = 5.11s making sense in this situation.
  • #1
sprinter08
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Homework Statement


A helicopter is ascending vertically with a speed of 5.5m/s. At a height of 100m above the Earth, a package is dropped from a window. How much time does it take the package to reach the ground?


Homework Equations


delta y = Vot + 1/2at^2


The Attempt at a Solution


well I know that:
Vo= 5.5m/s
a=-9.8 m/s^2
delta y= -100m

I re-wrote the equation so that I would solve it using the the quadratic formula.
-5.5 + the square root of (5.5)^2 -4(-4.9)(100)/ 2(-4.9)
My teacher gave us the answer of t= 5.11s, but I can't figure out how he did it.
 
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  • #2
Here's a site with the full quadratic formula: http://mathworld.wolfram.com/QuadraticFormula.html" . Just plug in the numbers and you'll get 2 solutions. Only one will make sense for this problem.
 
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  • #3
Your equation is not quite correct it's -5.5 plus or minus the sq rt...etc. You will get 2 values for t...which is correct? (also, be sure to check all math).
 

FAQ: When Does the Package Reach the Ground?

What is a helicopter and how does it work?

A helicopter is a type of aircraft that is capable of vertical takeoff and landing, as well as hovering in place. It uses rotating blades on top to generate lift and thrust, allowing it to move in any direction. The blades are controlled by the pilot through the use of a control stick and pedals, which change the pitch and angle of the blades to control the direction and speed of flight.

How is a package delivered by a helicopter?

A package can be delivered by a helicopter in several ways. It can be attached to the underside of the helicopter with a sling or harness and then dropped off at the desired location. Another method is by landing the helicopter at the delivery site and having a person or automated system unload the package from the cargo compartment. Some helicopters also have the capability to hover over a designated area and release the package via a winch system.

What types of packages can be delivered by a helicopter?

Helicopters have the ability to deliver a wide range of packages, from small letters and parcels to larger and heavier items. However, the size and weight limitations of a helicopter may vary depending on the type and model. Some helicopters are designed specifically for cargo transport and have larger cargo compartments, while others may only be able to carry smaller packages.

What are the advantages of using a helicopter for package delivery?

One of the main advantages of using a helicopter for package delivery is its ability to access remote or hard-to-reach locations. Helicopters can also deliver packages quickly and efficiently, as they are not bound by traffic or road conditions. Additionally, they can transport packages over long distances without the need for intermediate stops, making them ideal for urgent or time-sensitive deliveries.

Are there any disadvantages to using a helicopter for package delivery?

While helicopters have many advantages for package delivery, there are also some disadvantages to consider. Helicopter flights can be affected by weather conditions, such as strong winds or heavy rain, which may delay or cancel deliveries. The cost of using a helicopter for package delivery may also be higher compared to other modes of transportation, making it less feasible for regular or low-cost deliveries.

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