Question

Physics !!!!!!!!!!!!!!

Answer 1

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:

$I=\Delta p = m(v-u)$

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

$I=(45,000)(258-242)=720,000 kg m/s$

2)

The momentum of an object is given by

$p=mv$

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,

$p=(20)(0.75)=15 kg m/s$

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:

$p_i = 0$

while the total momentum after the shot is

$p_f = mv+MV$

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,

$p_i = p_f$

so we find:

$0=mv+MV\\V=\frac{-mv}{M}=\frac{-(70)(15)}{750}=-1.4 m/s$

Where the negative sign means the cannon moves in the direction opposite to the clown.

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