The range of projectile on a downward inclined plane is ________ the range on upward inclined plane for the same velocity of projection and angle of projection.

If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is

A

Zero

B

Maximum

C

Minimum

D

None of these

The direction of projection should bisect the angle between the inclined plane and the vertical for a range of a projectile on inclined plane

A

To be zero

B

To be maximum

C

To be minimum

D

None of these

The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be

A

$$\frac{{\sin \left( {\alpha + \beta } \right)}}{{\sin \left( {\alpha - \beta } \right)}}$$

B

$$\frac{{\sin \left( {\alpha - \beta } \right)}}{{\sin \left( {\alpha + \beta } \right)}}$$

C

$$\frac{{\cos \left( {\alpha - \beta } \right)}}{{\cos \left( {\alpha + \beta } \right)}}$$

D

$$\frac{{\tan \left( {\alpha - \beta } \right)}}{{\tan \left( {\alpha + \beta } \right)}}$$

For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is

A

$$\alpha = \frac{\pi }{4} - \frac{\beta }{2}$$

B

$$\alpha = \frac{\pi }{2} + \frac{\beta }{2}$$

C

$$\alpha = \frac{\beta }{2} - \frac{\pi }{2}$$

D

$$\alpha = \frac{\pi }{4} - \frac{\beta }{4}$$

E

$$\alpha = \frac{\pi }{2} - \frac{\beta }{2}$$

The range of projectile will be maximum for a given velocity of projectile, when the angle of projection ($$\alpha $$) is

A

$$\frac{\beta }{2}$$

B

30° + $$\frac{\beta }{2}$$

C

45° + $$\frac{\beta }{2}$$

D

60° + $$\frac{\beta }{2}$$

The range of projectile (R) on an upward inclined plane is

A

$$\frac{{{\text{g}}{{\cos }^2}\beta }}{{2{{\text{u}}^2}\sin \left( {\alpha + \beta } \right)\cos \alpha }}$$

B

$$\frac{{2{{\text{u}}^2}\sin \left( {\alpha + \beta } \right)\cos \alpha }}{{{\text{g}}{{\cos }^2}\beta }}$$

C

$$\frac{{{\text{g}}{{\cos }^2}\beta }}{{2{{\text{u}}^2}\sin \left( {\alpha - \beta } \right)\cos \alpha }}$$

D

$$\frac{{2{{\text{u}}^2}\sin \left( {\alpha - \beta } \right)\cos \alpha }}{{{\text{g}}{{\cos }^2}\beta }}$$

The time of flight of a projectile on downward inclined plane depends upon

A

Angle of projection

B

Angle of inclination of the plane

C

Both (A) and (B)

D

None of these

The velocity ratio in case of an inclined plane inclined at angle 'θ' to the horizontal and weight being pulled up the inclined plane by vertical effort is

A

sinθ

B

cosθ

C

tanθ

D

cosecθ

For a given velocity of a projectile, the range is maximum when the angle of projection is

A

30°

B

45°

C

90°

D

0°

The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be

A

[[[

The range of projectile on a downward inclined plane is ________ the range on upward inclined plane for the same velocity of projection and angle of projection.

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