Motion in a Plane Set-1

Q1. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

Q2. A ball is projected vertically upward with an initial velocity of $50 \text{ms}^{-1}$ at $t = 0s$. At $t = 2s$, another ball is projected vertically upward with same velocity. At $t =$ ______ s, second ball will meet the first ball ($g = 10 \text{ms}^{-2}$)

Q3. A body is projected from the ground at an angle of $45^\circ$ with the horizontal. Its velocity after $2s$ is $20 \text{ms}^{-1}$. The maximum height reached by the body during its motion is ______ m. (use $g = 10 \text{ms}^{-2}$)

Q4. A fighter jet is flying horizontally at a certain altitude with a speed of $200 \text{ms}^{-1}$. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle $\theta$ with the horizontal, to hit the jet. If the bullet speed is $400 \text{m/s}$, the value of $\theta$ will be…….

Q5. A projectile is launched at an angle $\alpha$ with the horizontal with a velocity $20 \text{ms}^{-1}$. After $10 s$, its inclination with horizontal is $\beta$. The value of $\tan\beta$ will be: ($g = 10 \text{ms}^{-2}$)

Q6. A girl standing on road holds her umbrella at $45^\circ$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2} \text{km/h}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

Q7. Motion of particle in $x$–$y$ plane is described by a set of following equations $x = 4 \sin \left( \frac{\pi}{2} - \omega t \right) \text{m}$ and $y = 4 \sin (\omega t) \text{m}$. The path of particle will be

Q8. A person can throw a ball upto a maximum range of $100 m$. How high above the ground he can throw the same ball?

Q9. A particle is moving in a straight line such that its velocity is increasing at $5 \text{ms}^{-1}$ per meter. The acceleration of the particle is ______ $\text{ms}^{-2}$ at a point where its velocity is $20 \text{ms}^{-1}$.

Q10. 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 range respectively will be

Q11. A ball is thrown vertically upwards with a velocity of $19.6 \text{ms}^{-1}$ from the top of a tower. The ball strikes the ground after $6 s$. The height from the ground up to which the ball can rise will be $\left(\frac{k}{5}\right) m$. The value of $k$ is ______ (use $g = 9.8 \text{m/s}^{-2}$)

Q12. A ball is projected from the ground with a speed $15\text{ms}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then ‘$\tan \theta$’ will be equal to

Q13. 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

Q14. If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y = 5x(1 - x)$. The $y$ component vector of the initial velocity is ______ $\hat{j}$. (Take $g = 10\text{m/s}^2$)

Q15. A body of mass $10 kg$ is projected at an angle of $45^\circ$ with the horizontal. The trajectory of the body is observed to pass through a point $(20, 10)$. If $T$ is the time of flight, then the momentum vector, at time $t = \frac{T}{\sqrt{2}}$, is ______ (Take $g = 10 \text{m/s}^2$)