A projectile is given an initial velocity of m/s, where is along the ground and is along the vertical. If , the equation of its trajectory is: [2012]

Question

A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10 {m/s}^{2}$ , the equation of its trajectory is: [2012]

Smart Achievers · Accepted Answer

(2)

$From equation, \vec{v} = \hat{i} + 2 \hat{j}$

$\Rightarrow x = t$ $. . . (i)$

$y = 2 t - \frac{1}{2} (10 t^{2})$ $. . . (i i)$

$From (i) and (ii), y = 2 x - 5 x^{2}$

Solution

Q.
A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10 {m/s}^{2}$ , the equation of its trajectory is: [2012]

1 $y = x - 5 x^{2}$

2 $y = 2 x - 5 x^{2}$

3 $4 y = 2 x - 5 x^{2}$

4 $4 y = 2 x - 25 x^{2}$

Ans.
(2)

$From equation, \vec{v} = \hat{i} + 2 \hat{j}$

$\Rightarrow x = t$ $. . . (i)$

$y = 2 t - \frac{1}{2} (10 t^{2})$ $. . . (i i)$

$From (i) and (ii), y = 2 x - 5 x^{2}$

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Solution

Q. A projectile is given an initial velocity of (i^+2j^)m/s, where i^ is along the ground and j^ is along the vertical. If g=10 m/s2, the equation of its trajectory is: [2012]

1 y=x-5x2

2 y=2x-5x2

3 4y=2x-5x2

4 4y=2x-25x2

Ans. (2) From equation, v→=i^+2j^ ⇒x=t ...(i) y=2t-12(10t2) ...(ii) From (i) and (ii), y=2x-5x2