1
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is -
A
$${{2R} \over g}$$
B
$${R \over g}$$
C
$${R \over {2g}}$$
D
$${R \over {4g}}$$
2
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2 . If it were launched at an angle $$\theta$$0 with speed v0 then (g = 10 ms–2) :
A
$${\theta _0} = {\cos ^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right)$$ and $${v_0} = {5 \over 3}$$ ms-1
B
$${\theta _0} = {\cos ^{ - 1}}\left( {{2 \over {\sqrt 5 }}} \right)$$ and $${v_0} = {3 \over 5}$$ ms-1
C
$${\theta _0} = {\sin ^{ - 1}}\left( {{2 \over {\sqrt 5 }}} \right)$$ and $${v_0} = {3 \over 5}$$ ms-1
D
$${\theta _0} = {\sin ^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right)$$ and $${v_0} = {5 \over 3}$$ ms-1
3
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
A plane is inclined at an angle $$\alpha$$ = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms–1 , from the base of the plane, making an angle $$\theta$$ = 15° with respect to the plane as shown in the figure. the distance from the base, at which the particle hits the plane is close to :
(Take g = 10 ms –2)
A
14 cm
B
18 cm
C
20 cm
D
26 cm
4
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to m$$\gamma$$u2 (where m is mass of the ball, u is its instantaneous velocity and $$\gamma$$ is a constant). Time taken by the ball to rise to its zenith is :
A
$${1 \over {\sqrt {\gamma g} }}{\tan ^{ - 1}}\left( {\sqrt {{\gamma \over g}} {V_0}} \right)$$
B
$${1 \over {\sqrt {\gamma g} }}{ln}\left( 1+ {\sqrt {{\gamma \over g}} {V_0}} \right)$$
C
$${1 \over {\sqrt {\gamma g} }}{\sin ^{ - 1}}\left( {\sqrt {{\gamma \over g}} {V_0}} \right)$$
D
$${1 \over {\sqrt {2\gamma g} }}{\tan ^{ - 1}}\left( {\sqrt {{2\gamma \over g}} {V_0}} \right)$$
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