 Hi and welcome to the session. Let's work out the following question. The question says, a particle is projected so as to graze the tops of two walls, each of height 10 meter at 15 meter and 45 meter respectively from the point of projection, find the angle of projection. So let the particle be projected so as to graze the tops of two walls, they are 10 meter and 10 meter high at 15 meter, that is the coordinates of this point will be 15, 10 and coordinate of this point will be 45, 10. Let us start with the solution to this question. First of all, let u be the velocity of projection and alpha be the angle of projection of the particle. Then the equation of trajectory is y equals to x tan alpha minus gx squared divided by 2 u squared, now it passes through the points 15, 10 and 45, 10 respectively. Therefore we have 10 is equal to 15 tan alpha minus 15 squared into g divided by 2 u squared cos squared alpha or we can say that 10 is equal to 15 tan alpha minus 225 g divided by 2 u squared cos squared alpha and this we call equation 1. Similarly, we have 10 is equal to 45 tan alpha minus squared of 45 is 2025, so 2025 g divided by 2 u squared cos squared alpha, this we call equation 2 from 1 and 2. We get 15 tan alpha minus 10 is equal to 225 g divided by 2 u squared cos squared alpha, this we call equation 3 and we also get 45 tan alpha minus 10 is equal to 2025 g divided by 2 u squared cos squared alpha and this we call equation 4. Now dividing equation 3 by 4 we get 10 tan alpha divided by, sorry this is 15 tan alpha minus 10 divided by 45 tan alpha minus 10 is equal to 225 g divided by 2 u squared cos squared alpha divided by 2 u squared cos squared alpha divided by 225 g. We see that this gets cancelled with this g with g and we have 15 tan alpha minus 10 divided by 45 tan alpha minus 10 is equal to 225 divided by 225. This is equal to 1 divided by 9. Now by cross multiplication we have 9 into 15 tan alpha minus 10 is equal to 45 tan alpha minus 10. This implies 135 tan alpha minus 45 tan alpha is equal to minus 10 plus 90. This implies 90 tan alpha is equal to 80. This implies tan alpha is equal to 80 over 90 that is equal to 8 divided by 9 and this implies that alpha is equal to tan inverse 8 upon 9. That means this angle alpha is tan inverse 8 upon 9 that is the angle of projection. So this is what you are supposed to find in this question. I hope that you understood the solution and enjoyed the session. Have a good day.