Question

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 varies with time t in seconds as :-

x = 10 (root3) t & y = 10t - t2

The maximum height attained by the ball is

(A) 100m

(B) 75m

(C) 50m

(D) 25m

Answer 1

GIVEN:-

x = 10 (root3) t

y = 10t - t2
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we know that you component of velocity is zero at maximum height

=>y = 10t - t2

=> Vy= 10-2t

=> at Max height, --->Vy = 0 = 10-2t

=> 2t = 10

=>t = 5 sec
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=> in time t=5s , body will cover Max height ..

=> y component of displacement at t=5s will give us Max height

=>y = 10t - t2

=> putting t=5sec-----> y = 10(5)-(5)^2

=> y=50-25

=> y=25m

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hope it helps you..
☺☺

Answer 2

$\frac{d}{dt} (y) = \frac{d}{dt} (10t) - \frac{d}{dt} (t {}^{2} ) = 10 - 2t$

At maximum height, V = 0

10 - 2t = 0

2t = 10

t = 5 s

Y = (10×5-5×5)m

= 25 m