Calculating Falling Object's Time to Reach Ground

[maca_404]

A helicopter is ascending vertically with a velocity of 12.5ms^-1. At a height of 120m above the ground a package is dropped out the door.

How long does it take for the package to reach the ground ?.


The attempt at a solution

I know

U = 12.5ms
A = -9.8ms
V = 0ms
S = 120m

Used t = v-u/a

T = 1.27 Seconds - the time it takes the object to stop ascending

Then used s = ut + .5 at^2 to find distance traveled

S = 7.97 meters

Adding this to the original height of 120m to get 127.97m

So now I have:

U = 0
A = 9.8ms
S = 127.97m

Use v^2 = u^2+2as to calculate the velocity after t

V = 50

Use V - U/A to get time

T = 5.1

Now I added the ascent and decent time to get total time before it hits the grounds

Total Time = 6.37 Seconds


Could someone look over this for me and tell me if I am even close to the correct answer ?.

Any help would be greatly appreciated

 

[azizlwl]

s=ut-0.5at^2
S is not a distance traveled but the displacement.
It is it's position with respect to the initial location.

 

[tiny-tim]

hi maca_404!

U = 12.5ms
A = -9.8ms
V = 0ms
S = 120m

no, V is not 0, is it?

 

[maca_404]

I had V as the velocity after t as it is ascending I assume it would need to be a two part calculations. The first when the object is ascending and being slowed by gravity at 9.8ms till its final velocity is 0 hence the V = 0 at the beginning. Then a second calculations starting from a zero velocity and then accelerating at 9.8ms towards earth. Is this not the correct procedure and can this be done with just one equation ?.

 

[tiny-tim]

… as it is ascending I assume it would need to be a two part calculations.

no

use azizlwl's standard constant acceleration equation, s= ut + 1/2 at²

 

[maca_404]

Thank you for the replies, I am more than a bit confused now I use this ballistic calculator online http://www.convertalot.com/ballistic_trajectory_calculator.html

Entering a initial velocity of 12.5ms and a starting height of 120m and a angle of 90Deg straight up the resulting answer is the same as I obtained originally.

Is my answer incorrect ?. Or am I just going about it the wrong way ?

Thanks Again

 

[tiny-tim]

Is my answer incorrect ?. Or am I just going about it the wrong way ?

i didn't check your original answer, as soon as i saw that you'd started the wrong way i stopped reading

your answer looks correct, but you won't get many marks in the exam for doing all that unnecessary work

try it the short way​