TE 4.6

(a) The maximum height of a projectile is directly proportional to the square of y-component of initial velocity of the projectile (see formula on page 97). Thus all three projectiles must have exactly the same y-components of the initial velocity. On the other hand, it means that they all have the same time of flight. Projectile (c) however has the greatest range, which means that it has the greatest x-component of velocity. Projectile (a) has the shortest range and consequently the lowest x-component of velocity. Since V₀² =  V_x0² + V_y0² projectiles in order of increasing initial speed are: (c), (b), (a).

(b) The time of flight is directly proportional to the y-component of the initial velocity (see formula 4-11 on page 91).   Since all three projectiles have the same y-component of initial velocity, they all have the same time of flight.