Walking through your neighborhood you notice Thor accidentally lose his hammer w

Question

Walking through your neighborhood you notice Thor accidentally lose his hammer while working on the roof. The hammer slides, starting from rest, a distance d down the roof which is angled theta from the vertical. (a) What is the speed of the hammer, as it leaves the roof, in terms of theta, d, g and the coefficient of kinetic friction between the roof and the hammer ?k. (b) If then the hammer slides off the roof from a height h, and lands a distance x from the base of the house, what is the speed it must have left the roof with in terms of theta, x, h, and the acceleration of gravity, g? (c) If the distance d down the roof is 8 m, the height h of the roof is 4 m, the angle? from the vertical of the roof is 55?, and the spot it lands on the ground is 2 m from the base of the roof, what is the coefficient of kinetic friction between hammer and the roof?

Explanation / Answer

v hor = 12.1m/s x cos 31 = 10.4m/s v vert = -12.1 m/s sin 31 = - 6.23m/s where the minus sign means the vertical velocity is down since the horizontal velocity will be the same throughout the flight, the horizontal distance will be hor dist = hor vel x time of flight so we find the time of flight from the y equation of motion y(t) = y0+ v0y t - 1/2 gt^2 y(t) = height at any time, t; v0y = initial vertical velocity = -6.23m/s; y0=initial height = 19.7m, g = accel due to gravity we want to know the time it takes for y(t) ->0, so we set y=0 and solve: 0 = 19.7 - 6.23 t - 4.9t^2 t = 1.47s therefore, the horizontal distance = 1.47s x 10.4m/s = 15.3m

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