JEE Mains · Physics · STD 11 - 3.2 motion in plane
A projectile is given an initial velocity of \((\hat i + 2\hat j)\ ms^{-1}\), 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
- A \(y= x- 5x^2\)
- B \(y= 2x- 5x^2\)
- C \(4y= 2x- 5x^2\)
- D \(4y= 2x- 25x^2\)
Answer & Solution
Correct Answer
(B) \(y= 2x- 5x^2\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l} \vec u = \hat i + 2\hat j = {u_x}\hat i + {u_y}\hat j \Rightarrow u\cos \theta = 1,\\ u\sin \theta = 2\\ y = x\tan \theta - \frac{1}{2}\frac{{g{x^2}}}{{u_x^2}}\\ \therefore \,y = 2x - \frac{1}{2}g{x^2} = 2x - 5{x^2} \end{array}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The election field in a region is given by \(\vec E = (Ax + B)\hat i\) where \(E\) is in \(N\,C^{-1}\) and \(x\) in meters. The values of constants are \(A = 20\, SI\, unit\) and \(B = 10\, SI\, unit\). If the potential at \(x =1\) is \(V_1\) and that at \(x = -5\) is \(V_2\) then \(V_1 -V_2\) is.....\(V\)JEE Mains 2019 Medium
- Two inclined planes are placed as shown in figure. A block is projected from the Point \(A\) of inclined plane \(A B\) along its surface with a velocity just sufficient to carry it to the top Point \(B\) at a height \(10 m\). After reaching the Point \(B\) the block slides down on inclined plane \(BC\). Time it takes to reach to the point \(C\) from point \(A\) is \(t (\sqrt{2}+1) s\). The value of \(t\) is........(use \(g =10 m / s ^{2}\) )
JEE Mains 2022 Hard - A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) isJEE Mains 2014 Hard
- In a nuclear fission reaction of an isotope of mass \(M\), three similar daughter nucler of same mass are formed. The speed of a daughter nuclei in terms of mass defect \(\Delta \mathrm{M}\) will be _______.JEE Mains 2024 Hard
- Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\)JEE Mains 2023 Hard
- \(I _{ CM }\) is moment of inertia of a circular disc about an axis \(( CM )\) passing through its center and perpendicular to the plane of disc. \(I _{ AB }\) is it's moment of inertia about an axis \(A B\) perpendicular to plane and parallel to axis \(CM\) at a distance \(\frac{2}{3} R\) from center. Where \(R\) is the radius of the disc. The ratio of \(I _{ AB }\) and \(I _{ CM }\) is \(x: 9\). The value of \(x\) is \(........\)
JEE Mains 2023 Medium
More PYQs from JEE Mains
- The sum of first \(9\) terms of the series \(\frac{{{1^3}}}{1} + \frac{{{1^3} + {2^3}}}{{1 + 3}} + \frac{{{1^3} + {2^3} + {3^3}}}{{1 + 3 + 5}} + .\;.\;.\;.\)JEE Mains 2015 Hard
- Two Carnot engines \(A\) and \(B\) are operated in series. Engine \(A\) receives heat from a reservoir at \(600\,K\) and rejects heat to a reservoir at temperature \(T\). Engine \(B\) receives; heat rejected by engine \(A\) and in turn rejects it to a reservoir at \(100\,K\). If the efficiencies of the two engines \(A\) and \(B\) are represented by \({\eta _A}\) and \({\eta _B}\) respectively, then what is the value of \(\frac{{{\eta _A}}}{{{\eta _B}}}\)JEE Mains 2018 Hard
- The point \((2, 1 )\) is translated parallel to the line \(L\) \(: x - y= 4\) by \(2\sqrt 3\,units\) . If the new points \(Q\) lies in the third quadrant, then the equation of the line passing through \(Q\) and perpendicular to \(L\) isJEE Mains 2016 Hard
- In a hydrogen like ion, the energy difference between the \(2^{\text {nd }}\) excitation energy state and ground is 108.8 eV. The atomic number of the ion isJEE Mains 2025 Medium
- Train \(A\) and train \(B\) are running on parallel tracks in the opposite directions with speeds of \(36\, km / hour\) and \(72 \,km / hour,\) respectively. A person is walking in train \(A\) in the direction opposite to its motion with a speed of \(1.8\, km / hr\). Speed (in \(ms ^{-1}\) ) of this person as observed from train \(B\) will be close to (take the distance between the tracks as negligible)JEE Mains 2020 Medium
- The number of 4-letter words, with or without meaning, which can be formed using the letters of 'PQRPQRSTUVP', is:JEE Mains 2026 Hard