An airplane flying with a velocity

In summary, an airplane flying at a velocity of 85.0 m/s at an angle of 19.0 degrees above the horizontal drops a suitcase out of its luggage compartment when it is 106 m directly above a dog standing on level ground. The question is asking for the distance from the dog where the suitcase will land, and the attempt at a solution involved using the equation Y-Yinitial = Voy(t) - 1/2(g)(t^2) to find the time, which was then multiplied by the horizontal velocity to find the range. However, the mistake was made of using 0 for the initial vertical velocity instead of 85m/s. The correct quadratic equation should be 0 = 105 +
  • #1
spacecadette
24
0
1. Homework Statement
An airplane is flying with a velocity of 85.0 m/s at an angle of 19.0 degrees above the horizontal. When the plane is a distance 106 m directly above a dog that is standing on level ground, a suitcase drops out of the luggage compartment.


2. Homework Equations
How far from the dog will the suitcase land? You can ignore air resistance.

3. The Attempt at a Solution
I attempted to use Y-Yinitial = Voy(t) - 1/2(g)(t^2)
I solved for t and i got t = 4.651 s.
That answer was incorrect.

I then tried using Vx = (85m/s)(cos19) = 80.37
Vy = (85m/s)(sin19) = 27.67

I then tried adding them using V = sqrt{(80.1^2) - (27.7^2)} = 75.16 m/s

I then did R = Vox(t) but the answer I got wasn't correct.
Help!
 
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  • #2
Welcome to PF.

The problem is that the vertical velocity continues to carry it upward before it goes down.

What if you reduced the problem to throwing a ball straight up at 27 m/s and you are standing on a 105m cliff? Find that time and multiply by the horizontal velocity.
 
  • #3
I'm still not sure how to solve this =(
 
  • #4
I attempted to use Y-Yinitial = Voy(t) - 1/2(g)(t^2)
I solved for t and i got t = 4.651 s.

You have the right method.

You got the wrong answer from the quadratic.
 
  • #5
Ohh! I didn't realize my mistake. I used 0 for Voy instead of 85m/s which is the initial velocity.
I solved the quadratic using the positive value and I got 1.168s. I then multiplied that by 85m/s to find the range and I got 99.28m. Does that sound correct?
 
  • #6
spacecadette said:
Ohh! I didn't realize my mistake. I used 0 for Voy instead of 85m/s which is the initial velocity.
I solved the quadratic using the positive value and I got 1.168s. I then multiplied that by 85m/s to find the range and I got 99.28m. Does that sound correct?

No.

Your initial vertical velocity is your Voy

Besides your quadratic should yield t to hit the ground. It can't get to the ground in 1 sec from 100 m.
 
  • #7
I'm sorry, I'm confused again.
 
  • #8
spacecadette said:
I'm sorry, I'm confused again.

Write out the equation for your quadratic. Let's see where you are going wrong.
 
  • #9
-85 (+ or -) sqrt{(-85^2) - 4(4.9)(-106) all divided by 2(4.9)

I think that when I added the -85 to the problem I ended up with 1.168

Now when I subtracted the -85 to the problem I got 18.51s. Which seems more realistic.
 
  • #10
spacecadette said:
-85 (+ or -) sqrt{(-85^2) - 4(4.9)(-106) all divided by 2(4.9)

I think that when I added the -85 to the problem I ended up with 1.168

Now when I subtracted the -85 to the problem I got 18.51s. Which seems more realistic.

But 85 is the velocity of the plane and it is not going straight up.

Your vertical component of velocity is 85*Sin19° = 27.67

That should yield 0 = 105 + 27.67*t -4.9*t2

That quadratic yields 8.246 s

I use this on-line calculator btw:
http://www.math.com/students/calculators/source/quadratic.htm
 
  • #11
Ohhh I understand now. Thank you so much for your help!
 
  • #12
How far from the dog will the suitcase land?

I'm still having issues finding the distance.
 
  • #13
spacecadette said:
How far from the dog will the suitcase land?

I'm still having issues finding the distance.

That's the easy part now.

You have time to hit the ground.
You have the horizontal velocity projected along the ground ...

Speed * time = distance.
 

Related to An airplane flying with a velocity

1. How does an airplane maintain its velocity during flight?

An airplane maintains its velocity by using the thrust generated by its engines to overcome the drag forces acting upon it. This allows the airplane to continue moving forward at a constant speed without slowing down or speeding up.

2. What factors affect an airplane's velocity during flight?

Several factors can affect an airplane's velocity during flight, including the angle of its wings, the altitude at which it is flying, the weight of the aircraft, and the speed and direction of the wind.

3. How does air resistance or drag impact an airplane's velocity?

Air resistance, also known as drag, acts in the opposite direction of an airplane's motion and can slow it down. This is why airplanes must constantly generate thrust to maintain their velocity and counteract the effects of drag.

4. Can an airplane's velocity change while in flight?

Yes, an airplane's velocity can change while in flight. Pilots can adjust the engine power and angle of the wings to change the airplane's speed and direction. Additionally, external factors such as wind can also cause changes in an airplane's velocity.

5. How is an airplane's velocity measured and monitored?

An airplane's velocity is typically measured and monitored using instruments such as airspeed indicators and GPS systems. These instruments provide real-time information on an airplane's speed and direction, allowing pilots to make adjustments as needed during flight.

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