A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec<sup>2</sup>)

The value of the expression:sin²1° + sin²11° + sin²21° + sin²31° + sin²41° + sin²45° + sin²49° + sin²59° + sin²69° + sin²79° + sin²89° is?

A

0

B

$${\text{5}}\frac{1}{2}$$

C

$${\text{4}}\frac{1}{2}$$

D

5

Flight to five different cities Mumbai, Delhi, Goa, Hyderabad, Bengaluru on five different days of week in a random order. Flight to Hyderabad is either on Friday or Saturday. There are no flights on Monday and Wednesday. Weekend flight are to Goa and Delhi. A day before a flight to Hyderabad, there is flight to Mumbai. Two days after the flight to Goa, there is flight to Bengaluru. There is a flight to Delhi on ....?

A

Sunday

B

Monday

C

Tuesday

D

Saturday

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

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

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

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 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

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

An object is projected at an angle θ into the atmosphere using a complex mechanism. The projectile travels with a specific velocity 'u' and makes an angle θ with the horizontal plane. In order for the projectile to travel maximum distance, the value of θ should be

A

30⁰

B

60⁰

C

45⁰

D

90⁰

In the following question, a given question is followed by information in two statements. You have to decide the data in which statement (s) is sufficient to answer the question and mark your answer accordingly. Amita, Priya, Sebastian, Trisha, Mauli, Jovita and Angelin have their flights to be departed from different airports such as Mumbai airport, Delhi airport, Chandigarh airport, Bangalore airport, Assam airport, Chennai airport and Amritsar airport. From which airport does Jovita’s flight depart? I. Trisha’s flight is from Assam airport. Mauli and Priya do not have their flights from Amritsar. Angelin’s flight is not from Chennai airport. II. Amita’s flight is from Bangalore airport. Jovita’s flight is not from Mumbai airport. Sebastian’s flight is departing from Delhi airport.

A

Statement I alone is sufficient while statement II alone is not sufficient.

B

Statement II alone is sufficient while statement I alone is not sufficient.

C

Either statement I alone or statement II alone is sufficient to answer the question.

D

Neither statement I nor statement II is sufficient to answer the question.

E

Both statement I and statement II together are necessary to answer the question.

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° + $$\frac{\beta }{2}$$

A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec²)

Related Questions

A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec2)

Related Questions

A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec²)