Respuesta :
The work should be at least equivalent to the kinetic energy possessed by the boat and its riders. The formula for kinetic energy is written below:
W = KE
W = 1/2*mv²
W = 1/2*(1,000 kg)(1.3 m/s)²
W = 845 J
W = KE
W = 1/2*mv²
W = 1/2*(1,000 kg)(1.3 m/s)²
W = 845 J
The work done by Sam to stop the coming boat in the amusement park is [tex]\boxed{845\,{\text{J}}}[/tex].
Further Explanation:
As the boat in the amusement park is moving at a certain velocity, the boat has the kinetic energy stored in it. This kinetic energy of the boat is due to the motion of the boat.
Sam needs to do the work against this energy of the boat to bring it to rest.
The initial kinetic energy of the boat is expressed as:
[tex]\begin{aligned}{K_i}&= \frac{1}{2}m{v^2}\\&=\frac{1}{2} \times 1000 \times {\left( {1.3} \right)^2}\\&= \frac{{1690}}{2}\,{\text{J}}\\&= 8{\text{45}}\,{\text{J}}\\\end{aligned}[/tex]
The boat is brought to rest finally. So, the final kinetic energy of the boat will be .
The amount of work required to be done by Sam will be equal to the change in kinetic energy of the boat.
[tex]\begin{aligned}W&= {K_f} - {K_i}\\&=0 - 845\\&=- 845\,{\text{J}}\\\end{aligned}[/tex]
Here, the negative work done means that the work is to be done by Sam on the boat in the opposite direction to stop it.
Thus, the work done by Sam to stop the coming boat in the amusement park is [tex]\boxed{845\,{\text{J}}}[/tex].
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Answer Details:
Grade: College
Subject: Physics
Chapter: Work-Energy Theorem
Keywords: Sam’s job, amusement park, slow down, boats in the long ride, kinetic energy, work done, boat drift at 1.3m/s, to stop the boat, energy stored in boat.
