Final Velocity Calculation for a Struck Ball

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The discussion centers on calculating the final velocity of a ball struck by a bat, with the ball initially moving at 10.0 m/s south and a force of 10 Ns applied. The user calculated a final velocity of 65.55 m/s, while the textbook states the correct answer is 45.555 m/s. The discrepancy arises from the misunderstanding of the impulse-momentum theorem, specifically the equation used. The correct application should consider the relative velocity as v + 10 m/s due to the opposing directions of the bat and ball.

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When a ball of mass 180 g is struck by a bat moving in the opposite direction,
the force acting on the ball is as shown in the graph (Figure 8.37). Determine
The final velocity of the ball if it was initially moving at
10.0 m s–1 south.

The graph depicted the Impulse as 10Ns (I checked the textbook and it was right)

However, when I calculated the final velocity, I got 65.55 and the answer in the textbook was 45.555

Ft = m(v-u)
10 = 0.180(v-10)
65.55 = v

Unless the Impulse is equation is Ft = m(u-v), i don't know how I got the answer wrong...
 
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Since the ball and the bat are moving in opposite directions, the relative velocity is v+10 not v-10 as you have.
 

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