Constant Acceleration and Free Fall Problem

[cheerspens]

1. Homework Statement
A package is dropped from a helicopter. Note that both the helicopter and package are traveling upward at 10.0m/s when the package is released. If the package takes 3.5 seconds to hit the ground, how high was the helicopter when the package was released?
If the helicopter's velocity does no change, how far above the ground will the helicopter be located when the package hits the ground?
What is the maximum height above the ground that this package reaches after it was released by the helicopter?

2. Homework Equations




3. The Attempt at a Solution
So far I've tried to answer the first two questions question and got that the helicopter was 25.025m high when the package was released and was 60.025m above the ground when the package hit the ground.

I made an x vs. t graph, a v vs. t graph, and an a vs. t graph to help with solving these as well.

So for the last question:
"What is the maximum height above the ground that this package reaches after it was released by the helicopter?"

Would the answer be 30.227m?

Thanks for your help!

 

[Delphi51]

All correct, I think. I get slightly different answers using g = 9.81 (29.9 for the last part).

 

[kerimek]

I would like to commend you on your attempt to solve this problem by creating graphs and using equations. Your answers for the first two questions seem correct based on the information given. However, it is important to note that this problem is an idealized scenario and does not take into account factors such as air resistance. In a real-world situation, the package would experience some air resistance and may not reach the maximum height of 30.227m.

To answer your third question, we can use the equation for displacement in free fall: d = vit + 1/2at^2. The package starts with an initial velocity of 10.0m/s and accelerates at a constant rate of 9.8m/s^2 (due to gravity). We can plug in the time of 3.5 seconds to find the maximum height: d = (10.0m/s)(3.5s) + 1/2(9.8m/s^2)(3.5s)^2 = 30.625m.

Therefore, the maximum height above the ground that the package reaches after it was released by the helicopter is approximately 30.6m. Again, this is an idealized scenario and the actual height may differ due to factors such as air resistance. Keep up the good work in solving problems using scientific methods!