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  4. A ball is projected from a certain point on the surface of a planet at a certain angle with the horizontal surface. The horizontal and vertical displacement x and y vary with time t (in seconds) as x=10√3t and y=10t-t2 . The maximum height attained by the ball is

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Q. A ball is projected from a certain point on the surface of a planet at a certain angle with the horizontal surface. The horizontal and vertical displacement $x$ and $y$ vary with time $t$ (in seconds) as $x=10\sqrt{3}t$ and $y=10t-t^{2}$ . The maximum height attained by the ball is

NTA AbhyasNTA Abhyas 2020Motion in a Plane

Solution:

$\frac{\text{dy}}{\text{dt}} = \text{v}_{\text{y}} = \text{10} - \text{2t}$
at maximum height $\text{v}_{y} = 0$
$t = 5 s$
So maximum height attained $\Rightarrow y_{\text{at} = 5} = \text{10 t} - \text{t}^{2}$
$= 50 - 25$
$= 25\, m$