question_answer

A ball is projected from the point O with velocity 20 m/s at an angle of 60° with horizontal as shown in the figure. At highest point of its trajectory, it strikes a smooth plane of inclination 30° at point A. The collision is perfectly inelastic. The maximum height from the ground attained by the ball is

A) 18.75m

B) 15m

C) 22.5m                   

D) 20.25m

Correct Answer: A

Solution :

Speed of ball before collision is \[\frac{\pi }{4}\]m/s Since, collision is perfectly inelastic (e = 0), so the ball will not bounce. It will move along the plane with velocity \[\frac{\pi }{3}\]m/s \[\frac{\pi }{2}\] Maximum height attained by the ball \[f(x)={{\log }_{5}}(25-{{x}^{2}})\] \[2x-y+z+3=0,\] \[r=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k})\]