To improve the jumping record, the long jumper should jump at an angle of:

Explanation

In projectile motion, the range R of a projectile is given by the formula R = (u² * sin 2θ) / g, where u is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. To maximize the range, the value of sin 2θ should be maximum, which is 1. This occurs when 2θ = 90°, hence θ = 45°. Therefore, an angle of 45° provides the largest possible range for a projectile. Angles lower than 45° reduce the vertical component too much, while angles greater than 45° reduce the horizontal component, both leading to a shorter range. Thus, option B is correct, while options A, C, and D do not provide the optimal angle for maximum range.