State the mathematical relationship between the maximum height \( H \) reached by an oblique projectile and its time of flight \( T \). [1 mark]

The maximum height \( H \) reached by an oblique projectile is given by the equation \( H = \frac{(v_0 \sin \theta)^2}{2g} \), where \( v_0 \) is the initial velocity, \( \theta \) is the launch angle, and \( g \) is the acceleration due to gravity. The time of flight \( T \) can be calculated as \( T = \frac{2 v_0 \sin \theta}{g} \). Therefore, while \( H \) and \( T \) are related through the initial parameters of the projectile's motion, they essentially capture different aspects of the projectile's trajectory. The relationship reveals that the time of flight directly influences how high the projectile can go, given the same initial speed and angle; a longer flight time typically means the projectile can reach a greater height, assuming it doesn't reach the peak too quickly before descending. This interplay makes predicting projectile motion a fun challenge!