a projectile is fired from the surface of the earth with a

A projectile is fired from the surface of the earth with a velocity of $$5\,m{s^{ - 1}}$$ at angle $$\theta $$ with the horizontal. Another projectile fired from another planet with a velocity of $$3\,m{s^{ - 1}}$$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $$m{s^{ - 2}}$$ ) is (given, $$g = 9.8\,m{s^{ - 2}}$$ )

A. $$3.5$$

B. $$5.9$$

C. $$16.3$$

D. $$110.8$$

Answer : $$3.5$$

Solution :
The trajectory of a projectile projected at some angle $$\theta $$ with the horizontal direction from ground is given by
$$y = x\tan \theta - \frac{{g{x^2}}}{{2{u^2}{{\cos }^2}\theta }}$$
For equal trajectories for same angle of projection,
$$\eqalign{ & \frac{g}{{{u^2}}} = {\text{constant}} \Rightarrow \frac{{9.8}}{{{5^2}}} = \frac{{g'}}{{{3^2}}} \cr & g' = \frac{{9.8 \times 9}}{{25}} = 3.5\,m{s^{ - 2}} \cr} $$

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Basic Physics >> Kinematics

Releted Question 1

A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-

A. Due north

B. $${30^ \circ }$$ East of north

C. $${30^ \circ }$$ West of north

D. $${60^ \circ }$$ East of north

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Releted Question 2

A boat which has a speed of $$5 km/hr$$ in still water crosses a river of width $$1 \,km$$ along the shortest possible path in $$15 \,minutes.$$ The velocity of the river water in $$km/hr$$ is-

A. 1

B. 3

C. 4

D. $$\sqrt {41} $$

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Releted Question 3

In $$1.0\,s,$$ a particle goes from point $$A$$ to point $$B,$$ moving in a semicircle of radius $$1.0 \,m$$ (see Figure). The magnitude of the average velocity-

A. $$3.14 \,m/s$$

B. $$2.0 \,m/s$$

C. $$1.0 \,m/s$$

D. Zero

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Releted Question 4

A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$ Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ above the ground as-

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Releted MCQ Question on
Basic Physics >> Kinematics

A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-

A boat which has a speed of $$5 km/hr$$ in still water crosses a river of width $$1 \,km$$ along the shortest possible path in $$15 \,minutes.$$ The velocity of the river water in $$km/hr$$ is-

In $$1.0\,s,$$ a particle goes from point $$A$$ to point $$B,$$ moving in a semicircle of radius $$1.0 \,m$$ (see Figure). The magnitude of the average velocity-

A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$ Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ above the ground as-

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Kinematics

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Releted MCQ Question on Basic Physics >> Kinematics

A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-

A boat which has a speed of $$5 km/hr$$ in still water crosses a river of width $$1 \,km$$ along the shortest possible path in $$15 \,minutes.$$ The velocity of the river water in $$km/hr$$ is-

In $$1.0\,s,$$ a particle goes from point $$A$$ to point $$B,$$ moving in a semicircle of radius $$1.0 \,m$$ (see Figure). The magnitude of the average velocity-

A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$ Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ above the ground as-

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