Question 150: Motion in 2D & Vectors

Question

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 ______________ $$\hat{j}$$. ($$\mathrm{Take}$$ $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

Accepted Answer

If the initial velocity in the horizontal direction of a projectile is represented by the unit vector $$\hat{i}$$ and the equation of the trajectory is given by $$y = 5x(1 - x)$$, we need to find the $$y$$ component vector of the initial velocity. (Given: $$g = 10 \mathrm{\ m/s^2}$$)
The trajectory equation can be expanded as:
$$y = 5x - 5x^2$$
In the general form of a projectile's trajectory: $$y = x 	an 	heta - \frac{1}{2} \frac{g x^2}{v_0^2}$$
Here, the equation compares as follows:
$$	an 	heta = 5 = \frac{u_y}{u_x}$$
Given that the initial horizontal velocity component, $$u_x$$, is 1 (unit vector $$\hat{i}$$), we can find $$u_y$$ from the relationship:
$$u_y = 5 	imes 1 = 5$$
Therefore, the $$y$$ component vector of the initial velocity is 5$$\hat{j}$$.

Motion in 2D & Vectors

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}. (\mathrm{Take} \left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)

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