Question 1 :
An artillary piece which consistently shoots its shells with the same muzzle speed has a maximum range R. To hit a target which is R/2 from the gun and on the same level, the elevation angle of the gun should be

Question 2 :
A truck travelling due north at {tex} 20 \mathrm { m } / \mathrm { s } {/tex} turns west and travels at the same speed. What is the change in velocity?

Question 3 :
If vectors {tex} \vec { P } = a \hat { i } + a \hat { j } + 3 \hat { k } {/tex} and {tex} \vec { Q } = a \hat { i } - 2 \hat { j } - \hat { k } \quad {/tex} are perpendicular to each other, then the positive value of {tex} a {/tex} is

Question 4 :
It is found that {tex} | \mathrm { A } + \mathrm { B } | = | \mathrm { A } | . {/tex} This necessarily implies,

Question 5 :
A particle is projected with a velocity {tex} v {/tex} such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

Question 6 :
A particle has an initial velocity {tex} 3 \hat { i } + 4 \hat { j } {/tex} and an acceleration of {tex} 0.4 \hat { i } + 0.3 \hat { j } . {/tex} Its speed after {tex}10 {/tex}sec is

Question 7 :
A particle moves in {tex} x {/tex} -y plane under the action of force {tex} \overrightarrow { \mathrm { F } } {/tex} and {tex} \overrightarrow { \mathrm { p } } {/tex} at a given time t {tex} \mathrm { p } _ { \mathrm { x } } = 2 \cos \theta , \mathrm { p } _ { \mathrm { y } } = 2 \sin \theta . {/tex} Then the angle {tex} \theta {/tex} between {tex} \overrightarrow { \mathrm { F } } {/tex} and {tex} \overrightarrow { \mathrm { p } } {/tex} at a given time t is:

Question 8 :
Which of the following vectors is perpendicular to the vector {tex} 4 \hat { i } - 3 \hat { j } ? {/tex}

Question 9 :
A stone tied to the end of a string of {tex} 1 \mathrm { m } {/tex} long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in {tex}44{/tex} seconds, what is the magnitude and direction of acceleration of the stone?