Question

$\huge\mathfrak\gray{☣Question}$
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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Answer 1

$Given : u_{y} = 0 \: \: \: \: a_{y} = g = 9.8m/ {s}^{2}$

$Let \: Initial \: Velocity \: be \: u$

$T = 3 \: Second \: \: \: ( Given )$

$T = \sqrt{ \frac{2h}{g} } ⟹h = \frac{ {gT}^{2} }{2}$

$h = \frac{9.8 \times {3}^{2} }{2} \\ = 44.1 \: m$

$x \: direction : a_{x} = 0⟹v _{x} = \: u$

$y \: direction \: :v_{y} = u_{y} + a_{y} T$

$v_{y} = 0 + 9.8 \times 3 \\ = 24.9 \: m/s$

$\frac{ V_{y} }{V_{x}} = Tan \: 45°= 1$

$V_{x} = V_{y} = 29.4 \: m/s$

$inital \: speed \: \: \: : u = V_{x} = 29.4m/s$