A model sailboat is slowly sailing west across a pond at 0.310 m/s. A gust of wind blowing at 28.3° south of west gives the sailboat a constant acceleration of magnitude 0.314 m/s2 during a time interval of 2.18 s. If the net force on the sailboat during the 2.18-s interval has magnitude 0.318 N, what is the sailboat's mass? What is the new velocity of the boat after the 2.18 s gust of wind?
Question
A model sailboat is slowly sailing west across a pond at 0.310 m/s. A gust of wind blowing at 28.3° south of west gives the sailboat a constant acceleration of magnitude 0.314 m/s2 during a time interval of 2.18 s. If the net force on the sailboat during the 2.18-s interval has magnitude 0.318 N, what is the sailboat's mass? What is the new velocity of the boat after the 2.18 s gust of wind?
Solution
First, let's find the mass of the sailboat. We know that force equals mass times acceleration (F = ma). We can rearrange this equation to solve for mass (m = F/a).
Given: Force (F) = 0.318 N Acceleration (a) = 0.314 m/s²
Substitute the given values into the equation:
m = F/a = 0.318 N / 0.314 m/s² = 1.01 kg
So, the mass of the sailboat is approximately 1.01 kg.
Next, let's find the new velocity of the boat after the 2.18 s gust of wind. We can use the equation for final velocity (v = u + at), where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given: Initial velocity (u) = 0.310 m/s Acceleration (a) = 0.314 m/s² Time (t) = 2.18 s
Substitute the given values into the equation:
v = u + at = 0.310 m/s + (0.314 m/s² * 2.18 s) = 0.994 m/s
So, the new velocity of the boat after the 2.18 s gust of wind is approximately 0.994 m/s.
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