During a soccer practice session, the football is positioned at the centre of the field 40 yards from the 10 ft high goalposts. A goal is attempted by kicking the football at a speed of 64 ft/s at an angle of 45^ to the horizontal. Will the ball reach the goal post?

Step-by-step solution

Given, initial speed u = 64 ft/s Angle of projection = 45^ Horizontal distance to goalposts x = 40 yards = 40 3 = 120 ft Acceleration due to gravity g = 32 ft/s ^2 The equation of trajectory is given by: y = x - g x^2 2 u^2 ^2 Substituting the values: y = 120 45^ - 32 (120)^2 2 (64)^2 ^2 45^ y = 120 (1) - 32 14400 2 4096 1 2 y = 120 - 14400 128 y = 120 - 112.5 = 7.5 ft Since the height of the ball is 7.5 ft , which is less than the goalpost height of 10 ft , the ball reaches the goalposts at a height of 7.5 ft .