Motion of a projectile thrown from a plane?

Question

A helicopter is flying horizontally at 7.7 m/s and an altitude of 16 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?

Answer 1

Pckage ground striking velocity= v
v=sqrt(2*g*h)
v=sqrt(2*10*16)
v=17.9 m/s
Time for package to hit ground=t
v=0.5*g*t^2
t=sqrt(v/(0.5*g))
t=sqrt(17.9/(0.5*10))
t=1.89 seconds
Helicopter travel = Sh
Sh=7*1.89
Sh=13.23 meters
Package ravel=Sp
Sp=13*1.89
Sp=24.57 meters
The separation distance= D
D= Sh+Sp
D=13.23+24.57
D=37.8 meters

Answer 2

like many ballistic problems, the first thing you have to do is find the time for the projectile to fall (or often rise and fall)

we are at 16 m, so ignoring for the time being, all the horizontal movement, we figure how long it takes something to fall 16 m

d=1/2at^2
16=1/2(9.8)t^2
3.3=t^2
1.8=t

I would usually show all the units on the various values to keep from making a conversion mistake but it is kind of hard to type all that

so, now we know it takes 1.8 seconds to fall to the ground (we know it is going horizontally relative to the ground but that doesn't affect the time it takes to fall, only where it finally falls)

how far will the package get from the helicopter (horizontally) in the 1.8 seconds?

well, the package and helicopter are separating at the package ejection speed relative to the helicopter (the fact that the helicopter is moving relative to the ground is irrelevant to how fast the package is moving compared to the copter, which is what we need to answer the question)

so, 13 m/s * 1.8 s = 5.4 m

when the package hits the ground, it is 5.4 meters behind the helicopter

I did this pretty quickly so you need to follow through it and check my arithmetic and the logic and the equations

hope this helps

good luck

Answer 3

simply by fact the equipment is thrown interior the choice direction of the action of helicopter the horizontal speed of the equipment could be 11- 8.3 = 2.7 m/s now, there isn't any downward speed. to that end the area traveled in downward direction is a million/2gt^2 a million/2gt^2 = 18. taking g = 9.eighty one we get t = a million.ninety two s so the horizontal distance coated is two.7 X a million.ninety two = 5.184 m.