Question

t="\huge \bf༆ question༄" align="absmiddle" class="latex-formula">
Three stones A, B , C are projected from surface of very long inclined plane with equal speeds and different angles of projection as shown in the figure. The incline makes an angle $\theta$ with horizontal. if $\sf {H_A , H_B and H_C}$ are maximum height attained by A, B and C respectively above inclined plane then choose the Correct choice among them ~

$\sf{H_A + H_C = H_B }$

$\sf{H_A {}^{2} + H_C {}^{2} } = H_B {}^{2}$

$\sf H_A + H_C = 2 H_B$

$\sf H_A {}^{2} + H_C {}^{2} = 2 H_B {}^{2}$
​

Answer 1

The resultant of the vectors is $H_A + H_C = H_B$.

What is a resultant vector?

A resultant vector is the vector sum of two or more vectors.

The given vectors;

• Height of vector A = HA
• Height of vector B = HB
• Height of vector C = HC

The height of vector B is the resultant of the three given vectors.

When the vectors are drawn from head to tail, the vector B forms the resultant of the two other vectors (A and C).

Thus, the resultant of the vectors is $H_A + H_C = H_B$.

Learn more about resultant vectors here: brainly.com/question/110151

Answer 2

$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Correct \: option \: is \: A) :-}}}}}}$

$\rule{300pt}{3pt}$

$\large{|\underline{\mathtt{\red{E}\blue{x}\orange{p}\pink{l}\blue{a}\purple{n}\green{a}\red{t}\blue{i}\green{o}\orange{n:-}}}}$

• $\large \tt \red {H_{B} = \frac{u ^{2} }{2g \sin \theta } }$

• $\large \tt \orange { H_{A} = \frac{u ^{2} \sin ^{2} \alpha }{2g \sin \theta} }$

• $\large \tt \blue { H_{C} = \frac{u ^{2} \sin ^{2} (90 - \alpha )}{2g \sin \theta} = \frac{u ^{2} \cos ^{2} \alpha }{2g \sin \theta } }$

$\large \tt \pink{⇒ H_{C} + H_{A} = H_{B}}$