What Is the Bird's Speed After Swallowing the Insect?

[jeeves_17]

A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it with a speed of 30m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the bird’s speed immediately after swallowing?



Relevant equations
Jx = m(Vx)f - m(Vx)i
Jy = m(Vy)f - m(Vy)i

Given
m(b) = 0.3 kg
v(b) = 6.0 m/s
m(i) = 0.01 kg
v(i) = 30 m/s



The attempt at a solution

Jx = (0.01)(30) - (0.3)(6.0)
= 0.12kg.m/s

0.12kg.m/s * 1/0.3kg = 0.4 m/s

?

 

[xcvxcvvc]

.3 * 6 - .01 * 30 = (.3 + .01) * v

conservation of momentum

p1 + p2 = p1' + p2'

forget the components in this problem. the objects are traveling in a linear path, so a negative value and a positive value denote the direction. You can assign what each equal, though, just as long as you keep it consistent throughout the problem.

 

[jeeves_17]

P1 = m1*v1
= (0.3)(6.0)
= 1.8

P2= m2*v2
= (0.01)(30)
=0.3

P1 +P2 = P3
1.8 +0.3 = P3
P3 = 2.1

P3 = m3v3
v3 = p3/m3
= 2.1/0.31
= 6.7741935
= 6.77 m/s?

 

[xcvxcvvc]

P1 = m1*v1
= (0.3)(6.0)
= 1.8

P2= m2*v2
= (0.01)(30)
=0.3

P1 +P2 = P3
1.8 +0.3 = P3
P3 = 2.1

P3 = m3v3
v3 = p3/m3
= 2.1/0.31
= 6.7741935
= 6.77 m/s?

No. p1 and p2 are vectors and in this problem they point exactly opposite of each other

Think about it this way: this interaction happens ONLY on the x axis, so only use the x axis.p1 = .3 * 6 * cos(0)
p1 = .3 * 6 * 1
p1 = 1.8
p2 = .01 * 30 * cos(180)
p2 = .01 * 30 * -1
p2 = NEGATIVE .3

p1 + p2 = p1' + p2'

1.8 + -.3 = (.01 + .3) * v(the v after the eating happens)

if v is negative, then the answer will be at 180. if positive, 0. (remember, only because i defined 0 degrees as positive velocity and 180 degrees as negative velocity)

The answer is 4.84 m/s, 0 degrees or "in the direction the bird was flying"The problem doesn't define a perspective, so you could say the bird was flying from right to left and all that would happen is the answer will be 180 degrees instead of 0. I would just include the degrees and the words to explain your perspective. Just think about it. You could watch this collision from any perspective. The result won't change, only the way to express it.

 

[ccc.sss]

just another way to do this is:


m1*(vf)1 + m2*(vf)2 = m1*(vi)1 + m2*(vi)2

because the bird swallows the insect (vf)1 and (vf)2 are going to be the same

(m1 + m2)*vf = m1*(vi)1 + m2*(vi)2

then solve for vf

vf= m1*(vi)1 + m2*(vi)2 divided by (m1 + m2)

to make things clear let's say the bird is flying in the positive direction, and since the insect is flying is the opposite direction of the bird making its velocity negative


sooo..

vf = (0.03kg * 6.0m/s) + (0.01kg * -30.0m/s) divided by (0.31kg)
vf= 4.8m/s