A ball is projected vertically downward with initial velocity 30 m/s from the top of the tower of height 80 m. Find the time taken by the ball to reach the ground.
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A ball is projected vertically downward with initial velocity 30 m/s from the top of the tower of height 80 m. Find the time taken by the ball to reach the ground.
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Verified answer
Given:
initial velocity 30 m/s
tower of height 80 m
To be found:
The time taken by the ball to reach the ground .
Formulas used
Kinematic equations for uniformly accelerated motion.
[tex]\bf\:v=u+at[/tex]
[tex]\bf\:s=ut+\frac{1}{2}at{}^{2}[/tex]
[tex]\bf\:v{}^{2}=u{}^{2}+2as[/tex]
and
[tex]\bf\:s_{nth}=u+\frac{a}{2}(2n-1)[/tex]
Solution
By equation of motion
[tex]\boxed{\bf S = ut +\frac{1}{2}a{t}^{2}}[/tex]
[tex]\implies \bf 80= 30t +5t^2 \\ \\ \implies \bf 5(t^2+6t-16)=0\\ \\ \implies \bf t^2+6t-16=0 \\ \\ \implies \bf (t+8)(t-2)=0 \\ \\ \implies \bf \boxed{\bf{t}}\ can't\ be\ negative \\ \\ So\ \boxed{\boxed{\bf t =2}}[/tex]
Hence,
The time is taken by the ball to reach the ground = 2 sec