Oblique Projectile Motion PYQs: JEE Mains Physics

Showing 1–35 of 35 questions

1. 1. Two identical bodies, projected with the same speed at two different angles cover the same horizontal range \(R\). If the time of flight of these bodies are \(5\) s and \(10\) s, respectively, then the value of \(R\) is ________ m. (Take \(g=10\) m/s\(^2\)) 2026 Medium
2. 2. Projectiles \(A\) and \(B\) are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection \(v_A: v_B\) is _______. 2024 Hard
3. 3. The angle of projection for a projectile to have same horizontal range and maximum height is _______. 2024 Hard
4. 4. The maximum height reached by a projectile is \(64 \mathrm{~m}\). If the initial velocity is halved, the new maximum height of the projectile is _______ \(\mathrm{m}\). 2024 Hard
5. 5. A particle of mass \(100\,g\) is projected at time \(t =0\) with a speed \(20\,ms ^{-1}\) at an angle \(45^{\circ}\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(t=2\,s\) is found to be \(\sqrt{ K }\,kg\,m ^2 / s\). The value of \(K\) is \(............\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)
   2023 Hard
6. 6. A projectile fired at \(30^{\circ}\) to the ground is observed to be at same height at time \(3 s\) and \(5 s\) after projection, during its flight. The speed of projection of the projectile is \(.........\,ms ^{-1}\)(Given \(g=10\,m s ^{-2}\) ) 2023 Hard
7. 7. A projectile is projected at \(30^{\circ}\) from horizontal with initial velocity \(40\,ms ^{-1}\). The velocity of the projectile at \(t =2\,s\) from the start will be \(........\) (Given \(g =10\,m / s ^2\) ) 2023 Hard
8. 8. A stone is projected at angle \(30^{\circ}\) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be : 2023 Medium
9. 9. Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a body is projected at an angle \(45^{\circ}\), it's range is maximum. Reason \(R\) : For maximum range, the value of \(\sin 2 \theta\) should be equal to one. In the light of the above statements, choose the correct answer from the options given below : 2023 Medium
10. 10. The initial speed of a projectile fired from ground is \(u\). At the highest point during its motion, the speed of projectile is \(\frac{\sqrt{3}}{2} u\). The time of flight of the projectile is: 2023 Medium
11. 11. The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\) 2023 Medium
12. 12. The range of the projectile projected at an angle of \(15^{\circ}\) with horizontal is \(50\,m\). If the projectile is projected with same velocity at an angle of \(45^{\circ}\) with horizontal, then its range will be \(........\,m\) 2023 Medium
13. 13. Two objects are projected with same velocity ' \(u\) ' however at different angles \(\alpha\) and \(\beta\) with the horizontal. If \(\alpha+\beta=90^{\circ}\), the ratio of horizontal range of the first object to the \(2^{\text {nd }}\) object will be : 2023 Medium
14. 14. Two projectiles \(A\) and \(B\) are thrown with initial velocities of \(40\,m / s\) and \(60\,m / s\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respectively is \(\left( g =10\,m / s ^2\right)\) 2023 Easy
15. 15. Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is: 2023 Easy
16. 16. A ball is projected from the ground with a speed \(15 \,ms ^{-1}\) at an angle \(\theta\) with horizontal so that its range and maximum height are equal, then \(tan\,\theta\) will be equal to  2022 Medium
17. 17. A ball is projected with kinetic energy \(E\), at an angle of \(60^{\circ}\) to the horizontal. The kinetic energy of this ball at the highest point of its flight will become. 2022 Medium
18. 18. A ball of mass \(m\) is thrown vertically upward. Another ball of mass \(2\,m\) is thrown an angle \(\theta\) with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is \(\frac{1}{x}\). The value of \(x\) is \(.....\) 2022 Medium
19. 19. A body is projected from the ground at an angle of \(45^{\circ}\) with the horizontal. Its velocity after \(2s\) is \(20 \,ms ^{-1}\). The maximum height reached by the body during its motion is \(m\). (use \(g =10\, ms ^{-2}\) ) 2022 Hard
20. 20. A projectile is launched at an angle ' \(\alpha\) ' with the horizontal with a velocity \(20 \; ms ^{-1}\). After \(10 s\), its inclination with horizontal is ' \(\beta\) '. The value of \(\tan \beta\) will be : \(\left( g =10 \; ms ^{-2}\right)\) 2022 Hard
21. 21. A projectile is projected with velocity of \(25\, m / s\) at an angle \(\theta\) with the horizontal. After t seconds its inclination with horizontal becomes zero. If \(R\) represents horizontal range of the projectile, the value of \(\theta\) will be : [use \(g =10 m / s ^{2}\) ] 2022 Medium
22. 22. An object is projected in the air with initial velocity \(u\) at an angle \(\theta\). The projectile motion is such that the horizontal range \(R\), is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be \(.......\) degree. 2022 Medium
23. 23. Given below are two statements. One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion A :Two identical balls \(A\) and \(B\) thrown with same velocity '\(u\) ' at two different angles with horizontal attained the same range \(R\). If \(A\) and \(B\) reached the maximum height \(h_{1}\) and \(h_{2}\) respectively, then \(R =4 \sqrt{ h _{1} h _{2}}\) Reason R: Product of said heights. \(h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)\) Choose the \(CORRECT\) answer  2022 Medium
24. 24. Two projectile thrown at \(30^{\circ}\) and \(45^{\circ}\) with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is 2022 Medium
25. 25. Two projectiles are thrown with same initial velocity making an angle of \(45^{\circ}\) and \(30^{\circ}\) with the horizontal respectively. The ratio of their respective ranges will be. 2022 Easy
26. 26. A player kicks a football with an initial speed of \(25\, {ms}^{-1}\) at an angle of \(45^{\circ}\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g \(=10 \,{ms}^{-2}\) ) 2021 Medium
27. 27. The projectile motion of a particle of mass \(5\, g\) is shown in the figure. The initial velocity of the particle is \(5 \sqrt{2}\, ms ^{-1}\) and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points \(A\) and \(B\) is \(x \times 10^{-2}\, kgms ^{-1} .\) The value of \(x ,\) to the nearest integer, is ...... .
    2021 Hard
28. 28. The ranges and heights for two projectiles projected with the same initial velocity at angles \(42^{\circ}\) and \(48^{\circ}\) with the horizontal are \({R}_{1}, {R}_{2}\) and \({H}_{1}\), \({H}_{2}\) respectively. Choose the correct option: 2021 Medium
29. 29. A body is projected at \(t = 0\) with a velocity \(10\,ms^{-1}\) at an angle of \(60^o\) with the horizontal. The radius of curvature of its trajectory at \(t=1\,s\) is \(R.\) Neglecting air resistance and taking acceleration due to gravity \(g = 10\,ms^{-2},\) the radius of \(R\) is   ........ \(m\) 2019 Hard
30. 30. A shell is fired from a fixed artillery gun with an initial speed \(u\) such that it hits the target on the ground at a distance \(R\) from it. If \(t_1\) and \(t_2\) are the values of the time taken by it to hit the target in two possible ways, the product \(t_1t_2\) is 2019 Hard
31. 31. The trajectory of a projectile near the surface of the earth is given as\( y = 2x -9x^2\). If it were launched at an angle \(\theta_0\) with speed \(v_0\) then \((g = 10\, ms^{-2}\)) 2019 Hard
32. 32. Two particles are projected from the same point with the same speed \(u\) such that they have the same range \(R\), but different maximum heights, \(h_1\) and \(h_2\). Which of the following is correct ? 2019 Hard
33. 33. A ball of mass \(160\, g\) is thrown up at an angle of \(60^o\) to the horizontal at a speed of \(10\, m\,s^{-1}\) . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ \(kg\, m^2/s\)  \((g\, = 10\, m\,s^{-2})\) 2014 Hard
34. 34. The position of a projectile launched from the origin at \(t = 0\) is given by \(\vec r = \left( {40\hat i + 50\hat j} \right)\,m\) at \(t = 2\,s\). If the projectile was launched at an angle \(\theta\) from the horizontal, then \(\theta\) is (take \(g = 10\, ms^{-2}\)) 2014 Hard
35. 35. A ball projected from ground at an angle of \(45^o\) just clears a wall in front. If point of projection is \(4\,m\) from the foot of wall and ball strikes the ground at a distance of \(6\,m\) on the other side of the wall, the height of the walI is  ........ \( m\) 2013 Hard

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