Questions: A Windy Day in a Boat Due in 5 hours, 3 minutes A boat has a mass of 6731 kg. Its engines generate a drive force of 4037 N, due west, while the wind exerts a force of 775 N, due east, and the water exerts a resistive force of 1210 N due east. What is the magnitude of the boat's acceleration? Submit Answer Tries 0/10

Solution Steps

The problem provides the following forces acting on the boat:

• Drive force by the engines: \( F_{\text{drive}} = 4037 \, \text{N} \) (due west)
• Wind force: \( F_{\text{wind}} = 775 \, \text{N} \) (due east)
• Water resistive force: \( F_{\text{water}} = 1210 \, \text{N} \) (due east)

The net force acting on the boat can be calculated by considering the direction of each force. Forces due west are positive, and forces due east are negative.

\[ F_{\text{net}} = F_{\text{drive}} - F_{\text{wind}} - F_{\text{water}} \]

Substitute the given values:

\[ F_{\text{net}} = 4037 \, \text{N} - 775 \, \text{N} - 1210 \, \text{N} = 2052 \, \text{N} \]

Using Newton's second law, the acceleration \( a \) of the boat can be calculated as:

\[ a = \frac{F_{\text{net}}}{m} \]

where \( m = 6731 \, \text{kg} \) is the mass of the boat.

Substitute the values:

\[ a = \frac{2052 \, \text{N}}{6731 \, \text{kg}} \approx 0.3048 \, \text{m/s}^2 \]

Final Answer