Question

A snowball rolls off a barn roof that slopes downward at an angle of α= 44.0∘ . (See the figure below) The edge of the roof is H= 14.0 m above the ground, and the snowball has a speed of v = 4.00 m/s as it rolls off the roof. Ignore air resistance.

Answer 1

The horizontal distance traveled  by the snowball is 4.11 m.

your question is not complete, it seems to be missing the following information;

how far does the ball travel horizontally ?

The given parameters;

• angle of inclination,  α = 44.0∘

• height of the roof, H = 14 m

• velocity of the ball, v = 4 m/s

The time of flight of the snowball is calculated as;

$h_y = v_0_yt + \frac{1}{2} gt^2\\\\14 = (4\times sin(44))t + 0.5\times 9.8t^2\\\\14 = 2.78t + 4.9t^2\\\\4.9t^2 +2.78t - 14 = 0\\\\solve \ the \ quadratic \ equation \ using \ formula \ method;\\\\a = 4.9, \ b = 2.78 ,\ c = -14\\\\t = \frac{-b \ \ +/- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\t = \frac{-2.78 \ \ +/- \ \ \sqrt{(2.78)^2 - 4(4.9\times -14)} }{2\times 4.9}\\\\t = 1.43 \ s$

The horizontal distance traveled  by the snowball is calculated as;

$X = v_0_x \times t\\\\X = (4 \times cos(44) ) \times 1.43\\\\X = 4.11 \ m$

Thus, the horizontal distance traveled  by the snowball is 4.11 m.

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