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+1 vote
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in Physics by (24.0k points)
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A projectile is given an initial velocity of i + 2j. The cartesian equation of its path is (Take g = 10 ms-2)

(a) y = x - 5x2 

(b) y = 2x - 5x2

(c) y = 2x - 15x2 

(d) y = 2x - 25x2

2 Answers

+3 votes
by (45.9k points)
selected by
 
Best answer

(b) y = 2x - 5x2

Explanation:

Given, \(\vec{u}\) = \(\hat{i}+2\hat{j}\) = ux\(\hat{i}\) + uy\(\hat{j}\)

Then ux = 1 = ucosθ  and

uy = 2 = usinθ

\(\therefore\) tanθ = \(\frac{u\sin\theta}{u\cos\theta}\) = \(\frac{2}{1}\) = 2

The equation of trajectory of a projectile motion is

y = x tanθ - \(\frac{gX^2}{2u^2\cos^2\theta}\)

= x tanθ - \(\frac{gX^2}{2(u\cos\theta)^2}\)

\(\therefore\) y = x * 2 - \(\frac{10\times X^2}{2(1)^2}\)

= 2x - 5x2

+4 votes
by (34.3k points)

Correct option (b) y = 2x - 5x2

Explanation :

The equation of trajectory of a projectile motion is

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