A pin fin of uniform, cross-sectional area is fabricated of an aluminum alloy ( 160 W/m·K). The fin diameter is 7 mm, and the fin is exposed to convective conditions characterized by 220 W/m2·K. It is reported that the fin efficiency is 0.65. Determine (a) the fin length and the fin effectiveness . Account for tip convection.

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

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As the ball rolls down the ramp, there are changes in kinetic and potential energy. how much kinetic energy does the ball have when it reaches point b? a) 0j b) 25j c) 50j d) 100