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GradeProjectile Motion, Projectile Motion, Projectile Motion

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A gun fires a bullet at a speed of $140m{s^{ - 1}}$ . If the bullet is to hit a target at the same level as the gun and at $1km$ distance, the angle of projection may be;

A. ${60^0}$ or ${30^0}$

B. ${40^0}$ or ${50^0}$

C. ${15^0}$ or ${75^0}$

D. ${20^0}$ or ${70^0}$

A. ${60^0}$ or ${30^0}$

B. ${40^0}$ or ${50^0}$

C. ${15^0}$ or ${75^0}$

D. ${20^0}$ or ${70^0}$

A small ball is projected up a smooth inclined plane with an initial speed of $10\,m{\text{ }}{s^{ - 1}}$ along the direction at ${30^ \circ }$ to the bottom edge of the slope. It returns to the edge after $2\,s$ . The ball is in contact with the inclined plane throughout the process. What is the inclination angle of the plane?

A particle of mass $m$, initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T$. It begins to move with a velocity u after the force stops acting. $F$ is shown in the graph as a function of time. The curve is a semicircle. Then:

$(A)u = \dfrac{{\pi F_o^2}}{{2m}}$

$(B)u = \dfrac{{\pi {T^2}}}{{8m}}$

$(C)u = \dfrac{{\pi {F_o}T}}{{4m}}$

$(D)u = \dfrac{{{F_o}T}}{{2m}}$

$(A)u = \dfrac{{\pi F_o^2}}{{2m}}$

$(B)u = \dfrac{{\pi {T^2}}}{{8m}}$

$(C)u = \dfrac{{\pi {F_o}T}}{{4m}}$

$(D)u = \dfrac{{{F_o}T}}{{2m}}$

A body is projected from ground at angle ${60^ \circ }$ with the horizontal. If it comes back to the ground at distance $60\sqrt 3 {\text{ }}m$ from the starting point then what is the time of flight?

A ball is thrown from a point with a speed ${V_0}$ at an angle of projected $\theta $. From the same point and at the same instant a person starts running with a constant speed $\dfrac{{{V_0}}}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

$\left( A \right)Yes,60^\circ $

$\left( B \right)Yes,30^\circ $

$\left( C \right)Yes,45^\circ $

$\left( D \right)No$

$\left( A \right)Yes,60^\circ $

$\left( B \right)Yes,30^\circ $

$\left( C \right)Yes,45^\circ $

$\left( D \right)No$

Show that the trajectory of a particle that is launched at an angle is parabolic?

A hose lying on the ground shoots a stream of water upward at an angle of \[40^\circ \] to the horizontal. The speed of the water is \[20\,m{s^{ - 1}}\] as it leaves the hose. How high up will it strike a wall which is \[8\,m\] away?

A particle of mass m is projected with initial speed u at an angle of $45$ degree with the horizontal. What is the torque of the force on the object about the point of projection at the highest point?

Two stones are projected from the same point with the same speed making angles $45^\circ + x$ and $45^\circ - x$ with the horizontal respectively. If $x \leqslant 45^\circ $ then the horizontal ranges of the two stones are in the ratio of?

Two particles move in a uniform gravitational field with an acceleration $g$ . At the initial moment the particles were located over a tower at one point and moved with velocities $v = 3\,m{s^{ - 1}}$ and $v = 4\,m{s^{ - 1}}$ horizontally in opposite directions. Find the distance between the particles at the moment when their velocity vectors become mutually perpendicular.

A. $2.5\,m$

B. $5\,m$

C. $8\,m$

D. none of the above

A. $2.5\,m$

B. $5\,m$

C. $8\,m$

D. none of the above

Prove that the maximum horizontal range is four times the maximum height attained by a projectile which is fired along the required oblique direction.

A shell fired from the ground is just able to cross in a horizontal direction the top of a wall $90m$ away and $45m$ high. The direction of projection of the shell will be

$\left( A \right)25^\circ $

$\left( B \right)30^\circ $

$\left( C \right)45^\circ $

$\left( D \right)none\,\,of\,these$

$\left( A \right)25^\circ $

$\left( B \right)30^\circ $

$\left( C \right)45^\circ $

$\left( D \right)none\,\,of\,these$

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