A ball is thrown from ground at an 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 $\frac{u_{0}}{α} .$ 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 0.8v₁ , the value of α is …….

Question

A ball is thrown from ground at an 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 $\frac{u_{0}}{α} .$ 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 0.8v₁ , the value of α is …….

Infinity Learn · Accepted Answer

before first hit with ground:T0=2u0sin⁡θg ; R0=u02sin2θg⇒vavg=R0T0=u02sin2θg2u0 sin⁡θg=u0cosθ⇒u0cos⁡θ=v1for a long time, m→∞vavg=R1+R2+R3+...t1+t2+t3+...⇒vavg=u02sin2θg+u02sin2θα2g+u02sin2θα4g+...2u0sin⁡θg+2u0sin⁡θαg+2u0sin⁡θα2g+...⇒vavg=u02sin2θg2u0sin⁡θg1+1α2+1α4+...1+1α+1α2+...⇒vavg=u cosθ 11-1α211-1α=v1 α1+α⇒v1 α1+α=0.8 v1⇒α=4

Start JEE / NEET / Foundation preparation at rupees 99/day !!

Detailed Solution

tricks from toppers of Infinity Learn

Get Expert Academic Guidance – Connect with a Counselor Today!