Answer :
Answer:
vf = 9.48 m/s
Explanation:
From the law of conservation of energy we can write:
[tex]Kinetic\ Energy\ Lost = Work\ Against\ Friction\\\frac{1}{2}m(v_i^2 - v_f^2) = fd\\\frac{1}{2}m(v_i^2 - v_f^2) = (\mu W)d\\\frac{1}{2}m(v_i^2 - v_f^2) = (\mu mg)d\\\frac{1}{2}(v_i^2 - v_f^2) = \mu gd\\v_f^2 = v_i^2 - 2\mu gd[/tex]
where,
vf = final speed = ?
vi = initial speed = 10.1 m/s
μ = coefficient of friction = 0.3
g = acceleration due to gravity = 9.81 m/s²
d = distance covered = 2.07 m
Therefore,
[tex]v_f^2 = (10.1\ m/s)^2 - 2(0.3)(9.81\ m/s^2)(2.07\ m)\\v_f^2 = 102.01\ m^2/s^2 - 12.18\ m^2/s^2\\v_f = \sqrt{89.83\ m^2/s^2}\\[/tex]
vf = 9.48 m/s