Question

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 = 10m/s² , the equation of its trajectory is [JEE main 2013] ​

Answer 1

Explanation:- As initial velocity V = (i+2j) m/s

for projectile

• Motion along horizontal direction
• x = t ______(1)
• motion along vertical direction
• y = ut - 1/2gt²
• where, u is a vertical component of velocity
• y = 2t -1/210t² _____(2)
• from eqs . (1) and (2) we get
• y = 2x - 5x²

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Answer 2

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Mass of two Satellites are of the ratio 3:1

✭ Radii of their circular orbit are in the ratio 1:4

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ Ratio of their total mechanical energy?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here to find the total energy we may use,

$\displaystyle\sf \underline{\boxed{\sf Total \ Energy = \dfrac{-GMm}{2r}}}$

Also let the two Bodies be A & B

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

We are given that,

⪼ $\displaystyle\sf \dfrac{m_1}{m_2} = \dfrac{3}{1}$

And,

⪼ $\displaystyle\sf \dfrac{r_1}{r_2} = \dfrac{1}{4}$

So then their total energy (E) will be,

➝ $\displaystyle\sf E_A = \dfrac{-GMm_1}{2r_1}$

And

➝$\displaystyle\sf E_B = \dfrac{-GMm_2}{2r_2}$

➳$\displaystyle\sf \dfrac{\dfrac{-GMm_1}{2r_1}}{\dfrac{-GMm_2}{2r_2}}$

➳$\displaystyle\sf \dfrac{m_1}{r_1} \times \dfrac{r_2}{m_2}$

➳ $\displaystyle\sf \dfrac{m_1}{m_2} \times \dfrac{r_2}{r_1}$

➳ $\displaystyle\sf \dfrac{3}{1}\times \dfrac{4}{1}$

➳ $\displaystyle\sf \dfrac{3\times4}{1}$

➳$\displaystyle\sf\pink{\dfrac{E_A}{E_B} = \dfrac{12}{1}}$

$\displaystyle\sf \therefore\:\underline{\sf Their \ Ratio \ will \ be \ E_A:E_B = 12:1}$

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