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

Explanation

improve the jumping record, the long jumper should jump at an angle of 45°.Here's why:Range of a projectile: The horizontal distance a projectile travels (its range) is maximized when the launch angle is 45 degrees, assuming the launch and landing points are at the same height and air resistance is negligible.Long jump as projectile motion: A long jump can be modeled as projectile motion. The jumper launches themselves at an angle, and their distance is determined by their initial velocity and launch angle.The formula for the range (R) of a projectile is:R = (v₀² * sin 2θ) / gWhere:v₀ is the initial velocityθ is the launch angleg is the acceleration due to gravityThe maximum value of sin 2θ is 1, which occurs when 2θ = 90°, or θ = 45°.While in real-world long jumping, factors like air resistance and the jumper's ability to generate both vertical and horizontal velocity play a role, the optimal theoretical launch angle for maximum distance is still 45°.