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

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.

A

Less than

B

More than

C

Equal to

D

None of these

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 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

The time of flight (t) of a projectile on a horizontal plane is given by

A

$${\text{t}} = \frac{{2{\text{u}}\sin \alpha }}{{\text{g}}}$$

B

$${\text{t}} = \frac{{2{\text{u}}\cos \alpha }}{{\text{g}}}$$

C

$${\text{t}} = \frac{{2{\text{u}}\tan \alpha }}{{\text{g}}}$$

D

$${\text{t}} = \frac{{2{\text{u}}}}{{{\text{g}}\sin \alpha }}$$

Time of flight of a projectile on a horizontal plane, is

A

$$\frac{{2{\text{u}}\sin \alpha }}{{\text{g}}}$$

B

$$\frac{{2{\text{u}}\cos \alpha }}{{\text{g}}}$$

C

$$\frac{{2{\text{u}}\tan \alpha }}{{\text{g}}}$$

D

$$\frac{{2{\text{u}}\cot \alpha }}{{\text{g}}}$$

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 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

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

A body of weight 'W' is required to move up on rough inclined plane whose angle of inclination with the horizontal is 'α'. The effort applied parallel to the plane is given by (where μ = tanφ = Coefficient of friction between the plane and the body.)

A

P = W tanα

B

P = W tan (α + φ)

C

P = W (sinα + μcosα)

D

P = W (cosα + μsinα)

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

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