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

If the velocity of projection is 4 m/sec and the angle of projection is $${\alpha ^ \circ }$$, the maximum height of the projectile from a horizontal plane, is

A

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

B

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

C

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

D

$$\frac{{{{\text{u}}^2}\sin2\alpha }}{{2{\text{g}}}}$$

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

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

If $${\text{tan }}\alpha = 2,$$ then the value of $$\frac{{{\text{cose}}{{\text{c}}^2}\alpha - {\text{se}}{{\text{c}}^2}\alpha }}{{{\text{cose}}{{\text{c}}^2}\alpha + se{c^2}\alpha }}$$ is?

A

$$ - \frac{5}{9}$$

B

$$\frac{3}{5}$$

C

$$ - \frac{3}{5}$$

D

$$\frac{{17}}{5}$$

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 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 8α9 = -72, -9α3 = 27 and -6α1 = 6, then find the value of -3α6 = ?

A

-98

B

-87

C

18

D

29

If 16α1 = 8, 14α6 = 42 and 12α5 = 30, then find the value of 2α6 = ?

A

6

B

18

C

4

D

10

If 18α1 = 34, 19α2 = 34 and 18α3 = 30, then find the value of 18α8 = ?

A

6

B

16

C

20

D

8

If 18α12 = 3, 2α14 = -6 and 4α4 = 0, then find the value of 2α16 = ?

A

-7

B

8

C

10

D

-1

If 6α1 = 70, 2α3 = 50 and 4α5 = 90, then find the value of 1α4 = ?

A

50 \

B

30 \

C

10 \

D

60

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

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