The vertical height reached by the block is 5.1 m
Explanation:
Assuming that the wood ramp is frictionless, we can solve the problem by applying the law of conservation of energy. In fact, the total mechanical energy of the block (the sum of its gravitational potential energy + its kinetic energy) must be conserved. Therefore 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 also rewritten as
[tex]mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2[/tex]
where:
m = 2 kg is the mass of the block
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]h_i = 0[/tex] is the initial height at the bottom
u = 10 m/s is the initial speed of the block
[tex]h_f[/tex] is the maximum height reached by the block
v = 0 is the final speed (which is zero at the maximum height)
And solving for [tex]h_f[/tex], we find: the vertical height reached by the block:
[tex]\frac{1}{2}mu^2 = mgh_f\\h_f = \frac{u^2}{2g}=\frac{(10)^2}{2(9.8)}=5.1 m[/tex]
Learn more about kinetic energy and potential energy:
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