[jengoesup]

Unfortunately I missed the review session for our physics test >> So I have some physics questions I'll be posting here. The first of these is:

An animal rescue plane flying due east at 36.0 m/s drops a bale of hay from an altitude of 60.0 m. If the bale of hay weighs 175 N, what is the momentum of the bale the moment it strikes the ground?

For some reason, in addition to the momentum the teacher gave me the angle at which it was below the horizon. Could someone please show me the work in detail to this problem? Please explain what all of your variables mean, just in case my text uses different variables.

Thanks!

[MrCrabby]

Well, when it hits the ground, it will have zero momentum.


Somehow, I doubt that was what you were looking for...

[jengoesup]

Well he really means the moment before it hits the ground...poorly worded question. The answer isn't zero, though.

[bobthecockroach]

Do you know if they just want the downward momentum? Otherwise, this could get messy.

[jengoesup]

I think they just want the downward momentum. I've typed the question exactly as my textbook has put it...the answer my teacher gave me was 888 kg x m/s at 43.6º below the horizon.

[jengoesup]

I just figured it out. hooray

[bobthecockroach]

Ok.

Force = mass * acceleration

Force = 175 N
Acceleration = 9.8 m/s²

Thus, mass = 175/9.8 = approximately 17.857 kg

Density = mass * velocity

To determine velocity, we need to know how long it takes the object to reach the ground.

Distance fallen = 1/2 g * t²

Where g is the acceleration of gravity (9.8m/s²) and t is time falling.

In other words:

time falling = sqrt(2*distance/g)

Distance = 60m

2d/g = approximately 12.245

sqrt(2d/g) = time falling = approximately 3.499

Now, we take the speed at 3.499 caused by the acceleration of gravity, which is simply the acceleration of gravity times the time.

9.8 * 3.499 = approximately 32.293 m/s

That's the velocity part of the momentum equation.

BUT, velocity is a vector, which means it also has a direction. To find the direction you will need to find the angle of impact based on an impact speed of 32.293 m/s down and 36.0 m/s east. To do this, you need to take the arctangent of 36/32.293, which is approximately 48.1 degrees, but I haven't the slightest idea how to report this in the answer.

In any event, the magnitude of the momentum is velocity times mass

32.293m/s * 17.857 kg = approximately 576.66 kg*m/s

[bobthecockroach]

Now I'm wondering how I got a different answer...

[bobthecockroach]

Yeah, ok, I forgot to combine the vectors before calculating the impact velocity.

[jengoesup]

Thanks for taking the time to figure it out *nod*

[MrCrabby]

Originally Posted by jengoesup

I just figured it out. hooray

Glad we could help.