Motion in a plane; projectile motion — practice questions

Question 1 · difficulty L2 · understanding

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$. $$\text { (take } \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 \text { ) }$$

Question 2 · difficulty L2 · understanding

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 ______ $$\mathrm{m}$$.

Question 3 · difficulty L2 · understanding

Two bodies are projected from ground with same speeds $40 \mathrm{~ms}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is $\mathrm{m}$. (Given $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

Question 4 · difficulty L2 · understanding

A fighter jet is flying horizontally at a certain altitude with a speed of 200 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 m/s, the value of $$\theta$$ will be ___________$$^\circ$$.

Question 5 · difficulty L2 · understanding

At $t=0$, a body of mass 100 g starts moving under the influence of a force $(5 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}) \mathrm{N} \cdot$ After 2 s its position is $(2 x \hat{\mathrm{i}}+5 y \hat{\mathrm{j}}) \mathrm{m}$. The ratio $x: y$ is $\_\_\_\_$ .

• A. $1: 2$
• B. $2: 5$
• C. $5 : 2$
• D. $5: 4$

Question 6 · difficulty L2 · understanding

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t-4.9 t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t=2 \mathrm{~s}$ is $\_\_\_\_$ .

• A. 60
• B. 45
• C. 30
• D. 75

Question 7 · difficulty L2 · understanding

The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1: x$. The value of $x$ is

• A. $\sqrt{2}$
• B. $$\sqrt{3}$$
• C. $2 \sqrt{3}$
• D. $$\frac{1}{\sqrt{2}}$$

Question 8 · difficulty L2 · understanding

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is : (use acceleration due to gravity g = 10 m/s 2 and neglect air resistance)

• A. 7.2 km
• B. 2$\sqrt{5}$ km
• C. 2$\sqrt{2}$ km
• D. 4 km

Question 9 · difficulty L2 · understanding

Two projectiles are fired from ground with same initial speeds from same point at angles $\left(45^{\circ}+\right.$ $\alpha)$ and $\left(45^{\circ}-\alpha\right)$ with horizontal direction. The ratio of their times of flights is

• A. $\frac{1+\tan \alpha}{1-\tan \alpha}$
• B. $\frac{1+\sin 2 \alpha}{1-\sin 2 \alpha}$
• C. $\frac{1-\tan \alpha}{1+\tan \alpha}$
• D. 1

Question 10 · difficulty L2 · understanding

A ball of mass 100 g is projected with velocity $20 \mathrm{~m} / \mathrm{s}$ at $60^{\circ}$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

• A. 20 J
• B. 5 J
• C. 15 J
• D. zero