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:
[tex]I=\Delta p = m(v-u)[/tex]
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
[tex]I=(45,000)(258-242)=720,000 kg m/s[/tex]
2)
The momentum of an object is given by
[tex]p=mv[/tex]
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,
[tex]p=(20)(0.75)=15 kg m/s[/tex]
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:
[tex]p_i = 0[/tex]
while the total momentum after the shot is
[tex]p_f = mv+MV[/tex]
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,
[tex]p_i = p_f[/tex]
so we find:
[tex]0=mv+MV\\V=\frac{-mv}{M}=\frac{-(70)(15)}{750}=-1.4 m/s[/tex]
Where the negative sign means the cannon moves in the direction opposite to the clown.
Learn more about momentum:
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