Hey There!
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Answer:
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DATA:
Initial velocity = [tex]V_0 = 50\frac{m}{s}[/tex]
Height = H = 100 m
Acceleration due to gravity = g = 10 m/s^2
Time of flight = ?
Angle of projection= θ(theta) = ?
Range attained = ?
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A) The Relation between Height and Total time of flight is given by,
[tex]T = 2(\sqrt\frac{2H}{g})\\\\T = 2( \sqrt\frac{2x100}{10})\\\\T = 2(\sqrt\frac{200}{10})\\\\T = 2(4.47)\\\\T = 8.94 seconds[/tex]
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B) Total time of flight is given by,
[tex]H = \frac{V_0^2Sin^2(theta)}{2g}\\\\100 x2x10 = 50^2Sin^2(theta)\\\\2000 = 2500Sin^2(theta)\\\\\frac{2000}{2500} = Sin^2(theta)\\\\Sin^2(theta)= \frac{4}{5}\\\\[/tex]
Square root on both sides,
[tex]Sin(theta) = \frac{2}{\sqrt{5}}\\\\theta = Sin^{-1}(\frac{2}{\sqrt{5} })\\\\theta = 63.4 degrees[/tex]
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C) The range attained is given by,
[tex]R = \frac{V_0^2}{g} xSin2(theta)\\\\R = \frac{50^2}{10} x Sin(2x63.4)\\\\R = 250 x 0.8\\\\R = 200meters[/tex]
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Best Regards,
'Borz'
