SATHEE: Kinematics 4 Question 9

Kinematics 4 Question 9

9. On a frictionless horizontal surface, assumed to be the $x - y$ plane, a small trolley $A$ is moving along a straight line parallel to the $y$ -axis (see figure) with a constant velocity of $(\sqrt{3} - 1) m / s$ . At a particular instant when the line $O A$ makes an angle of $45^{\circ}$ with the $x$ -axis, a ball is thrown along the surface from the origin $O$ . Its velocity makes an angle $φ$ with the $x$ -axis and it hits the trolley.

$(2002, 5$ M)

(a) The motion of the ball is observed from the frame of the trolley. Calculate the angle $θ$ made by the velocity vector of the ball with the $x$ -axis in this frame.

(b) Find the speed of the ball with respect to the surface, if $φ = 4 θ / 3$ .

(a) $6 m$

(b) $3 m$

(d) $9 m$

Show Answer

Solution:

Since, the body is at rest at $x = 0$ and $x = 1$ . Hence, $α$ cannot be positive for all time in the interval $0 \leq t \leq 1$ .

Therefore, first the particle is accelerated and then retarded.

Now, total time $t = 1 s$ (given)

Total displacement, $s = 1 m$ (given)

$s = Area under v - t graph$

$∴$ Height or $v_{max} = \frac{2 s}{t} = 2 m / s$ is also fixed.

$[Area or s = \frac{1}{2} \times t \times v_{max}]$

If height and base are fixed, area is also fixed .

In case $2 :$ Acceleration $=$ Retardation $= 4 m / s^{2}$

In case 1 : Acceleration $> 4 m / s^{2}$ while

Retardation $< 4 m / s^{2}$

While in case 3 : Acceleration $< 4 m / s^{2}$ and

Retardation $> 4 m / s^{2}$

Hence, $| α | \geq 4$ at some point or points in its path.

पिछला

अगला

Kinematics 4 Question 9

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Kinematics 4 Question 9

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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