K.E.

#526 / Dynamics Medium

A 50 kN speed boat is traveling at 40 kilometers per hour. What is its kinetic energy in kJ?

Expand Hint

$$$Force=mass\times acceleration$$$

Hint 2

Kinetic Energy:

$$$KE=\frac{1}{2}mv^2$$$

where $$m$$ is the mass and $$v$$ is the velocity.

In the problem statement, the weight of the speed boat is given as a force. To find the mass:

$$$F=m\times a$$$

where $$F$$ is the force, $$m$$ is the mass, and $$a$$ is the acceleration due to gravity. Thus,

$$$50kN=m\times 9.81\frac{m}{s^2}$$$

$$$m=\frac{50,000kg\cdot (m/s^2)}{9.81m/s^2}=5,096.84\:kg$$$

Next, convert the velocity into meters per second:

$$$40 \frac{km}{hr}\cdot \frac{1,000m}{km}\cdot \frac{hr}{60min}\cdot \frac{min}{60s}=11.11\:m/s$$$

Finally, to solve for Kinetic Energy:

$$$KE=\frac{1}{2}mv^2$$$

where $$m$$ is the mass and $$v$$ is the velocity.

$$$KE=\frac{1}{2}(5,096.84kg)(11.11m/s)^2=314,619.75\:kg\cdot \frac{m^2}{s^2}$$$

$$$=314,619.75N\cdot m=315\:kJ$$$

315 kJ

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