This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Relate the maximum horizontal range to the initial speed. The maximum horizontal range (R_max) for a projectile launched with an initial speed u occurs at a launch angle of 45^. The formula for maximum horizontal range is: R_max = (u^2)/(g) Given R_max = 100 m. 100 m = (u^2)/(g) From this, we can express u^2: u^2 = 100g Step 2: Calculate the maximum vertical height. To achieve the maximum vertical height (H_max), the ball must be thrown straight upwards, meaning the launch angle is 90^. The formula for maximum vertical height is: H_max = (u^2)/(2g) Substitute the expression for u^2 from Step 1 into this formula: H_max = (100g)/(2g) H_max = (100)/(2) H_max = 50 m The maximum height the player can throw the ball is 50 m. The final answer is 50 m.