Helicopter drops a package backwards.... yeah...?

Question

A helicopter is flying horizontally at 8.3 m/s and an altitude of 20 m when a package of emergency medical supplies is ejected horizontally backward with a speed of 13 m/s relative to the helicopter. Ignoring air resistance, what is the horizontal distance between the package and the helicopter when the package hits the ground?

I've tried to work this problem about 10 different ways, but nothing seems to work...

Answer 1

I disagree with the above answer, they feel that they do not need to take into account the distance the helicopter will fly during the time the package falls ..... I think that you do need to take this into account, as distances will be measured with respect to the earth ....

I believe you need to have the horiz speed measured with respect to [ wrt ] the ground ....... The package was moving 8.3 m/sec forwards with the helicopter [ which is measured wrt the ground ] ..... but then 13 m / sec backwards, wrt the helicopter [ you treat the helicopter as a stationary frame of reference ] ----> 13 - 8.3 = 4.7 m / sec backwards, wrt the ground.....

dist horiz = Vt, and since h = 0.5gt^2 ,
t = sqrt ( 2h / g) = sqrt ( 40 / 9.8 ) = 2.02 sec .... this is the time the package takes to fall to the ground ....
then d = ( 4.7 ) ( 2.02 ) = 9.5 m
from where it was released ... assuming it's horizontal velocity remains constant during it's fall .....

If you want the distance, horizontally from the helicopter to the package as it hits the ground, then add X = vt for the helicopter ....

x = [ 8.3 ] * [ 2.02 ] = 16. 8 m , this is how far the helicopter will fly while the package falls, assuming constant velocity ...

total distance = 16.8 + 9.5 = 26.3 meters , so the package should end up a total of 26.3 m behind the helicopter when it hits the ground ...

Answer 2

OK, the first thing to apply to this problem is the concept of motion.
Horizontal motion is entire independent of vertical motion. Hence, we first find the time taken by the package to reach the ground taking into account only its vertical motion.
acceleration of free fall,a = 10 m/s^2
intital vertical speed,u = 0 m/s
distance travelled,s = 20m
Let t be time taken,
s = ut + 1/2at^2
20 = (0)t + 1/2(10)(t)^2
20 = 5t^2
t^2 = 4
t = 2s.
That means to say that while travelling for 2s downwards, the package also travelled horizontally for 2 seconds.
therefore distance moved by package horizontally = 4.7*2 = 9.4m

meanwhile distance traveled by helicopter in 2 seconds
= 8.3*2
= 16.6m

horizontal distance between package and helicopter
=(16.6+9.4)m
=26m

Answer 3

first you need to work out how long it takes the package to fall.

S = ½ g t²
20 = ½ * 9,81 * t²
4,078 = t²
2 = t

the package takes 2 seconds to fall.

as the package is moving 13 meters relative to the helicopter, it is irrelevant to calculate how far the helicopter travels. simply calculate form the perspective of the helicopter.

13 meters a second. 2 seconds, equals 16 meters. the package will land 16 meters behind the helicopter.

Answer 4

Mr Zwink was correct when he didn't bother to look at the separate horizontal speeds, as the subsequent responder said was necessary, however he made a typo or arthmetical error right at the end. Should have been 26, not 16.

Of course maybe he did this so someone wouldn't be rewarded for cheating on what looks like a homework question.
Why are vwe helping them?

Answer 5

I hated while they used plane to contemporary physics issues. I had an entire blown communicate on the subject of a situation that for the duration of touch a x-wind. the subject replaced into provided as velocity over a floor , yet replaced into gazing velocity relative to apoint on the floor. for this question, its approx 22.14 m/s at time of result. For the genuine international, this does not be a at present vertical provide way. The rotorwash might accelerte the equipment via increasing downward tension on the field. to boot, by using winds, the equipment will additionally no longer fall at present down. floor component to the equipment might set off air resitance, and to get particularly clinical, being above the earth in a helicopter, counting on the place your at in the international, may be subjective to the corolis result. additionally, without parachute, the care equipment does not stay to tell the story anyhow as might hit around 50 mph. result might additionally be a reactionary tension, by using fact the collision might would desire to be an ellastic or inellastic gazing the floor decrease than.

Answer 6

Hints. Treat each direction separately. They are independent. That's how vectors work. How long does it take to hit the ground?

Um, Zwink. 13 m/s for two seconds gives 16m???