A girl throws a ball with initial velocity v at an inclination of $$45$$°. The ball strikes the smooth vertical wall at a horizontal distance d from girl and after rebounding returns to her hand. What is the coefficient of restitution between wall and ball ?

Question

A girl throws a ball with initial velocity v at an  inclination of $$45$$°. The ball strikes the smooth vertical wall at a horizontal distance d from girl and after rebounding returns to her hand. What is the coefficient of restitution between wall and ball ?

Infinity Learn · Accepted Answer

See fig.As the wall is smooth, the vertical component of the impulse it receives is zero, The total time of flight is given $$by0=vsin$$⁡$$45$$∘t−$$12gt2$$ or $$t=2vsin$$⁡$$45$$∘gThe time of flight $$t2$$ from G to $$A=dvcos$$⁡$$45$$∘The time of flight $$t2$$ from A to $$G=devcos$$⁡$$45$$∘where e $$=$$ coefficient of restitution. So, $$2v$$ $$sin$$⁡$$45$$∘$$g=dVcos$$⁡$$45$$∘$$+devcos$$⁡$$45$$∘or $$2vg=d2v+d2ev$$ $$vg=dV(1+1e)$$ or $$v2gd=1+1e$$ Solving, we get $$e=gdv2$$−gd.

A girl throws a ball with initial velocity v at an inclination of 45°. The ball strikes the smooth vertical wall at a horizontal distance d from girl and after rebounding returns to her hand. What is the coefficient of restitution between wall and ball ?

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