Answer:
The velocity of the boat 15 seconds later is 5.6 meters per second.
Explanation:
We assume that sailboat can be modelled as particle, so that we use solely translations equations. It is noticed that the sailboat is move by action of the wind and drag force of the water is opposed to such force, but the last force has a greater magnitude than the first one, meaning that net force is less than zero.
From Newton's Laws we have the following equation of equilibrium for the sailboat:
[tex]\Sigma F = F - f = m\cdot a[/tex] (Eq. 1)
Where:
[tex]F[/tex] - Force from the wind exerted on the sailboat, measured in newtons.
[tex]f[/tex] - Drag force of the water, measured in newtons.
[tex]m[/tex] - Mass of the sailboat, measured in kilograms.
[tex]a[/tex] - Net acceleration of the sailboat, measured in meters per square second.
If we know that [tex]F = 3.90\times 10^{3}\,N[/tex], [tex]f = 4.35\times 10^{3}\,N[/tex] and [tex]m = 1250\,kg[/tex], then the net acceleration of the sailboat is:
[tex]a = \frac{F-f}{m}[/tex]
[tex]a = \frac{3.90\times 10^{3}\,N-4.35\times 10^{3}\,N}{1250\,kg}[/tex]
[tex]a = -\frac{9}{25}\,\frac{m}{s^{2}}[/tex]
If sailboat decelerates uniformly, then we can get the final velocity of the boat by using this equation of motion:
[tex]v = v_{o}+a\cdot t[/tex] (Eq. 2)
Where:
[tex]v_{o}[/tex], [tex]v[/tex] - Initial and final velocities of the sailboat, measured in meters per second.
[tex]t[/tex] - Time, measured in seconds.
If we get that [tex]v_{o} = 11\,\frac{m}{s}[/tex], [tex]a = -\frac{9}{25}\,\frac{m}{s^{2}}[/tex] and [tex]t = 15\,s[/tex], then the final velocity of the sailboat is:
[tex]v = 11\,\frac{m}{s} +\left(-\frac{9}{25}\,\frac{m}{s^{2}} \right)\cdot (15\,s)[/tex]
[tex]v = 5.6\,\frac{m}{s}[/tex]
The velocity of the boat 15 seconds later is 5.6 meters per second.
The final velocity of the sailboat 15 seconds later is 5.6 m/s.
Given the following data:
To find the final velocity of the sailboat 15 seconds later:
First of all, we would determine the net force acting on the sailboat.
[tex]Net\;force = Forward\;force - Resistive\;force\\\\Net\;force = 3.90 \times 10^3 - 4.35 \times 10^3[/tex]
Net force = [tex]-4.35 \times 10^3[/tex] Newton.
Next, we would calculate the acceleration of the sailboat by applying Newton's Second Law of Motion:
[tex]Acceleration = \frac{Net\;force}{Mass} \\\\Acceleration = \frac{-0.45 \times 10^3}{1250}[/tex]
Acceleration = -0.36 [tex]m/s^2[/tex]
To calculate the final velocity of the boat 15 seconds later, we would use the first equation of motion:
[tex]V = U + at\\\\V = 11 + (-0.36)15\\\\V = 11 - 5.4[/tex]
Final velocity, V = 5.6 m/s
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