The height reached by the skateboarder is 1.41 m
Explanation:
We can solve this problem by using the law of conservation of energy. In fact, the mechanical energy of the skateboarder (which is the sum of his potential energy + his kinetic energy) must be conserved. So we can write:
[tex]U_i +K_i = U_f + K_f[/tex]
where
[tex]U_i[/tex] is the initial potential energy, at the bottom
[tex]K_i[/tex] is the initial kinetic energy, at the bottom
[tex]U_f[/tex] is the final potential energy, at the top
[tex]K_f[/tex] is the final kinetic energy, at the top
The equation can be rewritten as
[tex]mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2[/tex]
where:
m is the mass of the skateboarder
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]h_i = 0[/tex] is the initial height
u = 5.25 m/s is the initial speed
[tex]h_f[/tex] is the maximum height reached by the skateboarder
v = 0 is the final speed (zero at the maximum height)
Solving for [tex]h_f[/tex], we find:
[tex]\frac{1}{2}mu^2 = mgh_f\\h_f = \frac{u^2}{2g}=\frac{(5.25)^2}{2(9.8)}=1.41 m[/tex]
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