The only uniform acceleration (equal change in velocity for every equal intervals of time) acting in the entire situation is ‘acceleration due to gravity.’ Hence, kinematic equations can be used to proceed further since height is involved in the question.
Since time is not involved, by using the third equation, we can find the equation of the maximum height reached. For initial velocity and final velocity, we can consider only along the vertical axis since only the vertical component of velocity is required to reach the maximum height. At maximum height, the vertical component of velocity becomes zero. Hence, only the horizontal component of velocity will be the net velocity at maximum height.
From the formula derived by using the third kinematic equation, we can find two equations of maximum height for the two projectiles. Since the angles are complementary, there are two maximum height equations, one with the square of the sine function and the other with the square of the cosine function.
There are two unknowns, such as H1 and H2. So, to find the values of 2 maximum heights, two different equations are required. In the expression of H1 and H2, substitute the value of the initial velocity and the g (acceleration due to gravity) value. To get two equations, one equation is already given in the problem (the difference in heights is 5 meters), and the other equation can be obtained by adding H1 and H2. Solving two equations algebraically, the values are found.
