Motion in a Straight Line Set-1

Q1. A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$. [(JEE Main 2022)]

Q2. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws $n$ balls per second, the maximum height the balls can reach is [(JEE Main 2022)]

Q3. A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $h$. Find the ratio of the times in which it is at height $h / 3$ while going up and coming down respectively. [(JEE Main 2022)]

Q4. At time $t=0$ a particle starts travelling from a height $7 \ \mathrm{m}$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $\hat{i}$ and $\hat{j}$ directions are defined as $3t$ and $5t^3$ respectively. At $t = 1 \ \mathrm{s}$ acceleration of the particle will be [(JEE Main 2022)]

Q5. A NCC parade is going at a uniform speed of $9 \ \mathrm{km/h}$ under a mango tree on which a monkey is sitting at a height of $19.6 \ \mathrm{m}$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $g=9.8 \ \mathrm{m/s}^2$) [(JEE Main 2022)]

Q6. A bullet is shot vertically downwards with an initial velocity of $100 \ \mathrm{m/s}$ from a certain height. Within $10 \ \mathrm{s}$, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $t = 20 \ \mathrm{s}$ will be: (Take $g = 10 \ \mathrm{m/s}^2$) [(JEE Main 2022)]

Q7. 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 : [(JEE Main 2022)]

Q8. Two projectiles 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 : [(JEE Main 2022)]

Q9. A ball is projected from the ground with a speed $15 \ \mathrm{ms}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then '$\tan \theta$' will be equal to : [(JEE Main 2022)]

Q10. Two projectiles $P_1$ and $P_2$ thrown with speed in the ratio $\sqrt{3} : \sqrt{2}$, attain the same height during their motion. If $P_2$ is thrown at an angle of $60^\circ$ with the horizontal, the angle of projection of $P_1$ with horizontal will be : [(JEE Main 2022)]