A body is projected at time (t = 0) from a certain point on a planet’s surface with a certain velocity at a certain angle with the planet’s surface ( assumed horizontal). The horizontal and vertical displacements x & y (in meter) respectively vary with time t in second as, x = 10 \sqrt{3} \textrm{ } t and y = 10 t – t2. Then the maximum height attained by the body is :

Engineering

Physics

Projectile Motion

Question

A body is projected at time (t = 0) from a certain point on a planet’s surface with a certain velocity at a certain angle with the planet’s surface ( assumed horizontal). The horizontal and vertical displacements x & y (in meter) respectively vary with time t in second as, $x = 10 \sqrt{3} t$ and y = 10 t – t². Then the maximum height attained by the body is :

25 m

200 m

50 m

100 m

$y \max \Rightarrow \frac{dy}{dt} = 0$
⇒ 10 – 2t = 0
t = 5 sec.
y = 50 – 25 = 25 m

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