[tex] \huge\mathfrak\gray{☣Question}[/tex]
A stone is thrown horizontally from the top of the Cliff. It strikes the ground in 3 seconds at an angle of 45° with the horizontal. Determine the height of the tower and the speed of its projection?
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Verified answer
[tex]Given : u_{y} = 0 \: \: \: \: a_{y} = g = 9.8m/ {s}^{2} [/tex]
[tex]Let \: Initial \: Velocity \: be \: u[/tex]
[tex]T = 3 \: Second \: \: \: ( Given )[/tex]
[tex]T = \sqrt{ \frac{2h}{g} } ⟹h = \frac{ {gT}^{2} }{2} [/tex]
[tex]h = \frac{9.8 \times {3}^{2} }{2} \\ = 44.1 \: m[/tex]
[tex] x \: direction : a_{x} = 0⟹v _{x} = \: u[/tex]
[tex]y \: direction \: :v_{y} = u_{y} + a_{y} T[/tex]
[tex] v_{y} = 0 + 9.8 \times 3 \\ = 24.9 \: m/s[/tex]
[tex] \frac{ V_{y} }{V_{x}} = Tan \: 45°= 1[/tex]
[tex]V_{x} = V_{y} = 29.4 \: m/s[/tex]
[tex]inital \: speed \: \: \: : u = V_{x} = 29.4m/s[/tex]