Initial velocity of a projectile is (i + 2j) ms^{-1}, where i and j are unit vectors along horizontal and vertical

Question

Initial velocity of a projectile is \((\hat{i} + 2\hat{j})\ ms^{-1}\), where \(\hat{i}\) and \(\hat{j}\) are unit vectors along horizontal and vertical directions respectively. If g = 10 ms then equation of its path is:

(a) y = x - 5x²

(b) y = 2x - 5x²

(c) 4y = 2x - 5x²

(d) 4y = 2x - 25x²

Answer 1

Correct option is : (b) y = 2x - 5x²

Initial velocity \(\vec u = (\hat{i} + 2\hat{j})\ ms^{-1}\)

∴ Magnitude of \(\vec u\)

\(u = \sqrt{(1)^2 + (2)^2} = \sqrt{1 + 4} = \sqrt{5}\ ms^{-1}\) 

From the equation of trajectory

∴ Option (b) is correct.