A ball is thrown from ground at angle θ with horizontal and with an initial speed $$u0$$. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $$V1$$. After hitting the ground, the ball rebounds at the same angle θ but with a reduced speed of $$u0/$$α . Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $$0.8$$ $$V1$$, the value of α is $$_____$$

Question

A ball is thrown from ground at angle  θ with horizontal and with an initial speed $$u0$$. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $$V1$$. After hitting the ground, the ball rebounds at the same angle θ  but with a reduced speed of $$u0/$$α . Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $$0.8$$ $$V1$$, the value of α  is $$_____$$

Infinity Learn · Accepted Answer

$$R1=u02sin$$⁡$$2$$θ$$gR2=1$$α$$2u02sin$$⁡$$2$$θ$$g=R1a2$$ Total Range $$=R=R1+R1a2+$$…$$=R111$$−$$1a2=R1a2a2$$−$$1t1=2u0sin$$⁡θ$$gt2=t1$$α…… Total time of flight $$=T=t1+t2+$$…..$$=t111$$−$$1a=$$α$$t1$$α−$$1$$ Given : Average velocity $$=R1t1=v1$$ Total Average velocity $$=RT=R1a2a2$$−$$1at1a$$−$$1=R1t1$$×αα$$+1$$ Given :$$R1t1$$×αα$$+1=0.8R1t1$$⇒α$$=4$$

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