1) The impulse on the airplane is 720,000 kg m/s
2) The momentum of the cart is 15 kg m/s
3) The recoil velocity of the cannon is 1.4 m/s is the direction opposite to the clown
Explanation:
1)
The impulse exerted on an object is equal to the change in momentum of the object:
![I=\Delta p = m(v-u)](https://tex.z-dn.net/?f=I%3D%5CDelta%20p%20%3D%20m%28v-u%29)
where
m is the mass of the object
v is the final velocity
u is the initial velocity
For the airplane in the problem:
m = 45,000 kg
u = 242 m/s
v = 258 m/s
So, the impulse is
![I=(45,000)(258-242)=720,000 kg m/s](https://tex.z-dn.net/?f=I%3D%2845%2C000%29%28258-242%29%3D720%2C000%20kg%20m%2Fs)
2)
The momentum of an object is given by
![p=mv](https://tex.z-dn.net/?f=p%3Dmv)
where
m is the mass of the object
v is its velocity
In this problem, we have
m = 20 kg is the mass of the cart
v = 0.75 m/s is its velocity
Substituting,
![p=(20)(0.75)=15 kg m/s](https://tex.z-dn.net/?f=p%3D%2820%29%280.75%29%3D15%20kg%20m%2Fs)
3)
We can solve this problem by using the law of conservation of momentum: in fact, the total momentum of the cannon+clown system must be conserved before and after the shot.
Before the shot, the total momentum is zero, because they are both at rest:
![p_i = 0](https://tex.z-dn.net/?f=p_i%20%3D%200)
while the total momentum after the shot is
![p_f = mv+MV](https://tex.z-dn.net/?f=p_f%20%3D%20mv%2BMV)
where
m = 70 kg is the mass of the clown
v = 15 m/s is the velocity of the clown
M = 750 kg is the mass of the cannon
V is the recoil velocity of the cannon
Since the total momentum is conserved,
![p_i = p_f](https://tex.z-dn.net/?f=p_i%20%3D%20p_f)
so we find:
![0=mv+MV\\V=\frac{-mv}{M}=\frac{-(70)(15)}{750}=-1.4 m/s](https://tex.z-dn.net/?f=0%3Dmv%2BMV%5C%5CV%3D%5Cfrac%7B-mv%7D%7BM%7D%3D%5Cfrac%7B-%2870%29%2815%29%7D%7B750%7D%3D-1.4%20m%2Fs)
Where the negative sign means the cannon moves in the direction opposite to the clown.
Learn more about momentum:
brainly.com/question/7973509
brainly.com/question/6573742
brainly.com/question/2370982
brainly.com/question/9484203
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