1d Kinematics formula question

[RedBurns]

Could someone please help me in determine the correct formula(s) to answer this problem?

A helicopter is ascending vertically with a speed of 2.50 m/s. At a height of 120 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground?

I know:
Acceleration -9.8 m/s/s
Initial position 120m
Final postion 0m
velocity 2.50m/s

I need to determine time.

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Would 2.50/-9.8 give me the correct time of .26 seconds or have I missed something here?

or would I use 0=120 + 2.50T + .5(-9.8)T^2 giving the time of 50 seconds?

 

[tony873004]

Does 50 seconds seem reasonable?

 

[quicknote]

Based on your given information, the correct formula to use for this problem is the kinematic equation: h = h0 + v0t + 1/2at^2, where h is the final position, h0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time.

In this case, h = 0m (since the package reaches the ground), h0 = 120m, v0 = 2.50 m/s, and a = -9.8 m/s^2. Solving for t, we get:

0 = 120 + 2.50t + 1/2(-9.8)t^2
0 = 120 + 2.50t - 4.9t^2
4.9t^2 - 2.50t - 120 = 0

Using the quadratic formula, we get two possible solutions: t = 6.13 seconds or t = -3.89 seconds. Since time cannot be negative, the correct answer is t = 6.13 seconds.

So, to answer your question, using the formula 2.50/-9.8 would not give you the correct time. And using 0=120 + 2.50T + .5(-9.8)T^2 would give you the correct time if you solve for t correctly.

 

[kyle8921]

I would suggest using the second formula you mentioned: 0=120 + 2.50T + .5(-9.8)T^2. This is the correct formula to use for solving this problem as it takes into account the initial position, final position, initial velocity, and acceleration. The first formula you mentioned, 2.50/-9.8, only calculates the time for the package to reach the ground if it had no initial velocity, which is not the case in this scenario. So, using the second formula will give you a more accurate and precise answer. The final answer should be approximately 5.46 seconds.