The engine of a 2280 kg boat exerts a 1800 N force northward, while a current pushes the boat 1050 N eastward. What is the magnitude of the acceleration of the boat? $$ \mathrm{a}=[\text { ? }] \mathrm{m} / \mathrm{s}^{2} $$ $$ \begin{array}{l}\text { Remember to indicate if the acceleration } \ \text { is positive ( }+ \text { ) or negative }(-) \text {. }\end{array} $$

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We first determine the net force acting on the boat using vector addition. The force components are:  
- Northward: $$ F_N = 1800 \, \text{N} $$  
- Eastward: $$ F_E = 1050 \, \text{N} $$

1. **Calculate the magnitude of the net force:**  
   Using the Pythagorean theorem,  
   $$
   F_{\text{net}} = \sqrt{F_N^2 + F_E^2} = \sqrt{(1800)^2 + (1050)^2}
   $$
   
   Compute the squares:  
   $$
   (1800)^2 = 3240000, \quad (1050)^2 = 1102500
   $$
   
   Sum the squares:  
   $$
   3240000 + 1102500 = 4342500
   $$
   
   Take the square root:  
   $$
   F_{\text{net}} = \sqrt{4342500} \approx 2084.37 \, \text{N}
   $$

2. **Determine the acceleration:**  
   Using Newton's second law,  
   $$
   a = \frac{F_{\text{net}}}{m}
   $$
   where $$ m = 2280 \, \text{kg} $$. Substitute the values:
   $$
   a = \frac{2084.37 \, \text{N}}{2280 \, \text{kg}} \approx 0.913 \, \text{m/s}^2
   $$

3. **Indicate the sign of the acceleration:**  
   Since both force components are given in their respective positive directions (north and east), the acceleration components are positive. However, the magnitude of the acceleration is a positive quantity.

The magnitude of the acceleration of the boat is  
$$
\boxed{0.913 \, \text{m/s}^2}
$$
The boat's acceleration is approximately $$ 0.913 \, \text{m/s}^2 $$ to the north and east.

The engine of a 2280 kg boat exerts a 1800 N
force northward, while a current pushes the
boat 1050 N eastward.
What is the magnitude of the
acceleration of the boat?

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