Range on an Incline

Q. If $R_1$ and $R_2$ are the maximum ranges of a projectile when it is projected from the bottom and top respectively of an inclined plane respectively, then find the maximum range of the projectile when it is projected from the ground with same velocity.

1. $\frac{R_1+R_2}{2}$
2. $\frac{R_1{R}_2}{R_1+R_2}$
3. $\frac{2R_1{R}_2}{R_1+R_2}$
4. $\frac{R_1+R_2}{R_1{R}_2}$

Q.

Which of the path (I) or (II) of a projectile has more time of flight? Use necessary assumptions.

1. Data insufficient

2. >

3. <

4. =

Q. A plane is inclined at an angle $\alpha ={30}^{\circ }$ with respect to the horizontal. A particle is projected with a speed $u=2\text{m/s}$, from the base of the plane, making an angle $\theta ={15}^{\circ }$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to [Take $g=10\text{m}/s^2]$

1. $26cm$
2. $20cm$
3. $18cm$
4. $14cm$

Q. Time taken by the projectile to reach from $A$ to $B$ is $t$. Then, the distance $AB$ is equal to

1. $\frac{ut}{\sqrt{3}}$
2. $\frac{\sqrt{3}ut}{2}$
3. $\sqrt{3}ut$
4. $2ut$

Q. An inclined plane makes as angle ${\theta }_0={30}^{\circ }$ with the horizontal. A particle is projected from this plane with a speed of $5\text{m/s}$ at an angle of elevation $\beta ={30}^{\circ }$ with the horizontal as shown in the figure.


Find the range of the particle on the plane when it strikes the plane. (Assume the incline is long enough and $g=10{\text{m/s}}^2$)

1. $3.5\text{m}$
2. $4\text{m}$
3. $4.2\text{m}$
4. $5\text{m}$

Q. A plane surface is inclined making an angle $\theta$ with the horizontal. From the bottom of this inclined plane, a bullet is fired with velocity $v$. The maximum possible range of the bullet on the inclined plane is

1. $\frac{v^2}{g}$
2. $\frac{v^2}{g(1+\sin \theta )}$
3. $\frac{v^2}{g(1-\sin \theta )}$
4. $\frac{v^2}{g(1+\cos \theta )}$

Q. A plane surface is inclined making an angle $\theta$ with the horizontal. From the top of this inclined plane, a bullet is fired with velocity $v$. The maximum possible range of the bullet on the inclined plane is

1. $\frac{v^2}{g}$
2. $\frac{v^2}{g(1+\sin \theta )}$
3. $\frac{v^2}{g(1-\sin \theta )}$
4. $\frac{v^2}{g(1+\cos \theta )}$

Q. Two balls are thrown from an inclined plane at angle of projection $\alpha$ with the plane one up the incline plane and other down the incline as shown in the figure. If $R_1$ & $R_2$ be their respective ranges and $h_1$ & $h_2$ be their respective maximum height then
[here $T_1$ & $T_2$ are times of flight in the two cases respectively]

1. $h_1=h_2$
2. $R_2-R_1=T_1^2$
3. $R_2-R_1=\text{g sin}\theta T_2^2$
4. $R_2-R_1=\text{g sin}\theta T_1^2$