Question

1. a 10.0 kg cannonball is fired from a 145 kg cannon with a force of 850.0 n to the east. what is the acceleration of the cannon? 5.86 m/s² to the east 85.0 m/s² to the west 5.86 m/s² to the west 85.0 m/s² to the east

Explanation:

Step1: Apply Newton's third law

When the cannon fires the cannon - ball, the force exerted on the cannon - ball (\(F = 850.0\ N\) east) has an equal and opposite reaction force on the cannon. So the force on the cannon \(F_{cannon}=850.0\ N\) west.

Step2: Use Newton's second law \(F = ma\)

We know \(F_{cannon}=850.0\ N\), \(m = 145\ kg\). Rearranging \(a=\frac{F}{m}\) for the cannon's acceleration. Substitute \(F = 850.0\ N\) and \(m = 145\ kg\) into the formula: \(a=\frac{850.0}{145}\)

$$a=\frac{850.0}{145}\approx5.86\ m/s^{2}$$

The direction is west (opposite to the direction of the force on the cannon - ball)

Answer:

5.86 m/s² to the west