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

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

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 time of flight (t) of a projectile on an upward inclined plane is (where u = Velocity of projection, $$\alpha $$ = Angle of projection and $$\beta $$ = Inclination of the plane with the horizontal.)

A

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

B

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

C

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

D

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

The time of flight (t) of a projectile on an upward inclined plane is
(where u = Velocity of projection, $$\alpha $$ = Angle of projection and $$\beta $$ = Inclination of the plane with the horizontal.)

A

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

B

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

C

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

D

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

if A B C D and E are points in a plane such that the line CD bisects angle ACb and line CB bisects right angle ACE ,then DCE=?

A

45 deg

B

22.5 deg

C

65.5 deg

D

85 deg

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

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

This are the following statements given regarding satellite’s motion a. A satellite in geostationary orbit lies in the same plane with equator b. A satellite in geosynchronous orbit lies in the same plane with equator c. A satellite in geostationary orbit does not lie in the same plane with equator, it is inclined at some angle from plane of equator d. A satellite in geosynchronous orbit does not lie in the same plane with equator, it is inclined at some angle from plane of equator Choose one of the following options

A

Both option a and b are correct

B

Both option a and c are correct

C

Both option a and d are correct

D

Both option b and c are correct

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° + $$\frac{\beta }{2}$$

If the angle of projection is double the angle of inclination (α) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be

A

½ cos α

B

½ sin α

C

½ tan α

D

2 cos α

If the angle of projection is double the angle of inclination ($$\alpha $$) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be

A

$$\frac{1}{2}\,\cos \alpha $$

B

$$\frac{1}{2}\,\sin \alpha $$

C

$$\frac{1}{2}\,\tan \alpha $$

D

$$2\cos \alpha $$

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

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