If the initial velocity in horizontal direction of a projectile is unit vector $\hat{\mathrm{i}}$ and the equation of trajectory is $\mathrm{y}=5 \mathrm{x}(1-\mathrm{x})$. The y component vector of the initial velocity is \_\_\_\_ $\hat{\mathrm{j}}$ (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Kinematics

If the initial velocity in horizontal direction of a projectile is unit vector

\hat{i}

and the equation of trajectory is

y = 5 x (1 - x)

. The y component vector of the initial velocity is ____

\hat{j}

(Take

g = 10 m / s^{2}

)

Answer: 5

Solution

Given

u_{x} = 1

and trajectory

y = 5 x (1 - x)

.

Differentiating with respect to time:

\frac{d y}{d t} = 5 \frac{d x}{d t} - 10 x \frac{d x}{d t}

x = 0

(initial position), the y-component of velocity is:

u_{y} = (\frac{d y}{d t})_{x = 0} = 5 \times 1 = 5

Therefore,

u_{y} = 5 \hat{j}

, and the answer is 5.

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Integer answer

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