K.E.
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
Time Analysis
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