First slide

Motion in a plane

Question

A particle is moving in xy plane and equation of its trajectory is $y = (120 x - 3 x^{2})$ where x and y are in metre. When the distance of the particle from x-axis is maximum, speed of the particle is

Moderate

A

2 m/s
B

1 m/s
C

0.5 m/s
D

1.5 m/s

Solution

When distance from x-axis is maximum, velocity component along y-axis must be zero.
i.e. $\frac{d y}{d t} = 0$ i.e. $120 - 3 \times 2 x \frac{d x}{d t} = 0 \Rightarrow \frac{d x}{d t} = \frac{20}{x}$
Again, when y is maximum, $\frac{d y}{d x} = 0 \Rightarrow 120 - 6 x = 0 \Rightarrow x = 20 m$
$∴ \frac{d x}{d t} = \frac{20}{20} m / s = 1 m / s$

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