Kinematics

JEE Main level, numerical answer, medium

240 of 308

Question 240 of 308

If the initial velocity in horizontal direction of a projectile is unit vector i^\hat{i} and the equation of trajectory is y=5x(1−x)y=5x\left(1-x\right). The yy component vector of the initial velocity is _____ j^\hat{j}
(Take g=10ms−2g=10m{s}^{-2})

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Answer: 5

Given here, initial velocity, ux=1{u}_{x}=1
Equation of trajectory, y=5x(1−x)=5x−5x2y=5x\left(1-x\right)=5x-5{x}^{2}
Now, differentiating the above equation,
dydt=5dxdt−10xdxdt\dfrac{dy}{dt}=5\dfrac{dx}{dt}-10x\dfrac{dx}{dt}
For initial yy-component of velocity
uy=(dydt)x=0⇒5(1)=5{u}_{y}={\left(\dfrac{dy}{dt}\right)}_{x=0} \Rightarrow 5\left(1\right)=5
u⃗y=5j^{\vec{u}}_{y}=5\hat{j}

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