 Hello and welcome to the session, let us discuss the following question. It says a particle is projected so as to graze the tops of two walls each of height 10 meter and at 15 meter and 45 meter respectively from the point of projection. Find the angle of projection. Let us now move on to the solution and let u be the velocity of the projection of projection. Equation of the trajectory is y is equal to alpha minus gx square upon 2u square into cos square alpha. Now we are given that the particle is projected so as to graze the tops of the two walls each of height 10 meter. So particle is projected from a point say o and it grazes the tops of two walls each of height 10 meter at 15 meter and 45 meter from the point of projection. If we assume that this is the x axis this is the y axis. So this point would be 15 10 and this would be 45 10 that means a particle passes through the point 15 10 and 45 10 put x is equal to 15 and y is equal to 10 in this. So we have 10 is equal to 15 tan alpha minus gx square x is 15 upon 2u square cos square alpha let us now simplify this more further. So we have 10 is equal to 15 tan alpha minus 15 square is 225 g upon 2u square minus cos square alpha. Let us name this as 2. Now again we will put x is equal to 45 and y is equal to 10 in this. So we have 10 is equal to 45 tan alpha minus 45 square g upon 2u square cos square alpha. Now again this is equal to tan is equal to 45 tan alpha minus 45 square is 2025 into g upon 2u square cos square alpha. Let us name this as 3. Now from n3 we have 15 tan alpha minus 10 is equal to 225 g upon 2u square cos square alpha. Similarly we have 45 tan alpha minus 10 is equal to 2025 g upon 2u square cos square alpha. Let us name this as 4 and this is 5. Now dividing 5 by 4 we have 45 tan alpha minus 10 upon 15 tan alpha minus 10 is equal to 2025 upon 225. So this implies 45 tan alpha minus 10 upon 15 tan alpha minus 10 is equal to 9. So this implies 45 tan alpha minus 10 is equal to 9 into 15 tan alpha minus 10 and this implies 45 tan alpha minus 10 is equal to 135 tan alpha minus 90 and this implies 135 tan alpha minus 45 tan alpha is equal to 90 minus 10 and this implies 90 tan alpha is equal to 80 and this implies tan alpha is equal to 80 upon 90. 0 gets cancelled with 0 and this implies alpha is equal to tan inverse 8 by 9. Hence the angle of projection inverse 8 by 9. So this completes the question and the session. Bye for now. Take care. Have a good day.