The coefficient of restitution for a body is e=(1/3) . At what angle the body must be incident on a perfectly hard plane so that the angle between the direction before and after the impact be at right angles?

Question

The coefficient of restitution for a body is e=(1/3) . At what angle the body must be incident on a perfectly hard plane so that the angle between the direction before and after the impact be at right angles? (A) 37°  (B) 60°  (C) 45°  (D) 30°

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-r4bjzt1umm63v2hh.jpg" /> tan φ=(1/e)tan â¡ θ Given θ +φ=90° ∴ tan (90 ° - θ )=(1/((1)3))tan â¡ θ cot θ ((1/3))=tan â¡ θ tan2 θ =(1/3) tan θ =(1/√3) θ =30°

Q. The coefficient of restitution for a body is $e = \frac{1}{3}$ . At what angle the body must be incident on a perfectly hard plane so that the angle between the direction before and after the impact be at right angles?

$3 7^{\circ}$

$6 0^{\circ}$

$4 5^{\circ}$

$3 0^{\circ}$

$t an ϕ = \frac{1}{e} t an θ$
Given $θ + ϕ = 9 0^{\circ}$
$∴ t an (9 0^{\circ} - θ) = \frac{1}{( \frac{1}{3} )} t an θ$
$co tθ (\frac{1}{3}) = t an θ$
$t a n^{2} θ = \frac{1}{3}$
$t an θ = \frac{1}{3}$
$θ = 3 0^{\circ}$

Q. The coefficient of restitution for a body is e=31​ . At what angle the body must be incident on a perfectly hard plane so that the angle between the direction before and after the impact be at right angles?

37∘

60∘

45∘

30∘