Motion in 2D - Test with Audio Solutions 2

The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = 8 t - 5 t^{2} m$ and x = 6t m, where t is in seconds. The velocity with which the particle is projected is.
1. 14 m/s
2. 10 m/s
3. 8 m/s
4. 6 m/s

A particle of mass m is projectile with a velocity v making an angle of $30^{o}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of the projection when particle is at it's maximum height h is
$1 . \sqrt{\frac{3}{2}} \frac{m v^{2}}{g}$
$2 . z e r o$
$3 . \frac{m v^{3}}{\sqrt{2} g}$
$4 . \frac{\sqrt[]{} 3}{16} \frac{m v^{3}}{g}$

if a person can through a stone to maximum height of h meter vertically, then maximum distance through which it can be thrown horizontally by the same person is
1. h/2
2. h
3. 2h
4. 3h

At the top of the trajectory of a projectile, direction of its velocity and acceleration are
1. perpendicular to each other
2. parallel to each other
3. inclined to each other at angle of $45^{0}$
4. antiparallel to each other

These particles A, B and C are projected from the same pair with same initial speed making angles $30^{o,} 45^{o} & 60^{o}$ respectively with the horizontal. Which of the following statements is correct .
1. A, B and C have unequal ranges
2. Range of A and C are less than that of B
3. Range of A and C are equal & greater than that of B
4. A, B and C have equal ranges

At the height 80 m an aeroplane is moving with 150m/s. A bomb is dropped from it, so as to hit a target. At what distance from the target should bomb be dropped ?
1. 605.3 m
2. 600 m
3. 80 m
4. 230 m

Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground, their velocities are $v_{1}, v_{2} & v_{3}$ respectively , than
$1 . v_{1} > v_{2} > v_{3}$
$2 . v_{3} > v_{2} > v_{1}$
$3 . v_{1} = v_{2} = v_{3}$
$4 . v_{1} < v_{2} < v_{3}$

An object of mass 2m is projected with a speed of 100 m/s at an angle $θ = \sin^{- 1} (\frac{3}{5})$ to the horizontal. At the highest point, the object breaks into pieces of same mass m & the first one comes to rest . The distance between point of landing of the bigger piece is (given g = 10 m/s² )
1. 3840 m
2. 1280 m
3. 1440 m
4. 960 m

A cart is moving horizontally along a straight line with contant speed of 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the cart) must the projectile be fired ? (given g = 10 m/s²)
1. 10 m/s
2. $\frac{40}{3} m / s$
3. $10 \sqrt{8} m / s$
4. None of the above

10.

A body is projected with velocity u at an angle $θ$ with horizontal from a moving cart then path of the body appears to be

1.	Straight line for observer on ground, parabola for observer in cart.
2.	Straight line for observer in cart as well as observer on ground.
3.	Parabola for observer on cart and parabola of lesser angle for observer on ground.
4.	None of the above.

11.

A cart is moving with speed of 20m/s on a horizontal track. A body is projected with speed 40m/s (relative to cart ) from the cart in such a way that path of body appear to be straight line for an observer on ground. Time for which body remains in air is:
$1 . 2 \sqrt{3} s e c$
$2 . 4 s e c$
$3 . 4 \sqrt{3} s e c$
$4 . 8 s e c$

12.

Two particles A and B are projected with velocity $u_{1} a n d u_{2}$ simultaneously. Time after which they start moving perpendicularly to each other is ?
$1 . \frac{\sqrt{u_{1} u_{2}}}{g}$
$2 . \frac{2 \sqrt{u_{1} u_{2}}}{g}$
$3 . \frac{\sqrt{u_{1} u_{2}}}{2 g}$
$4 . \frac{\sqrt{2 u_{1} u_{2}}}{g}$

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