Answer :
Final answer:
Using the law of conservation of momentum, we find that the speed of the potato as it exits the cannon is approximately 290.32 m/s. This calculation assumes no external forces are acting on the system. The masses of the cannon and potato, along with the recoil speed of the cannon, were used to derive this result.
Explanation:
Calculating the Speed of the Potato Leaving the Cannon
In this problem, we apply the law of conservation of momentum to find the speed at which the potato leaves the cannon. The law states that the total momentum before an event must equal the total momentum after the event, provided no external forces act on the system.
In our scenario, we define the mass and speed of the cannon and the potato:
- Mass of potato, mp = 124 g = 0.124 kg
- Mass of cannon, mc = 15 kg
- Speed of cannon after firing, vc = -2.4 m/s (the negative sign indicates that the cannon moves in the opposite direction to the potato)
Let vp be the speed of the potato as it leaves the cannon. According to conservation of momentum:
Initial Momentum = Final Momentum
Initially, when both the cannon and potato are at rest, the momentum is:
0 = mp vp + mc vc
Substituting our known values:
0 = (0.124 kg vp) + (15 kg -2.4 m/s)
This simplifies to:
0.124 vp = 15 * 2.4
0.124 vp = 36
Now solving for vp:
vp = 36 / 0.124
vp ≈ 290.32 m/s
Thus, the speed at which the potato leaves the cannon is approximately 290.32 m/s.
Learn more about momentum here:
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