Answer: the ball clears the bar by 2.48[m] as it passes through the goal posts.
Step-by-step explanation:
This question requires you to solve for two quantities. First you will need to determine how long it takes the ball to reach the goal based on its x-velocity. Second, you will use the time you calculated to determine the y-value (height) of the ball at that time. Putting these values together, you will know by how much the ball cleared the goal post.
Step 1: Finding how long it takes to reach the goal post.
1. Convert the speed of 17[m/s] into its x-component and y-component.
2. The x-component is given by 17*cos(59.4) = 8.654[m/s]
3. The y-component is given by 17*sin(59.4) = 14.633 [m/s] (Note that it makes sense that the y-component is larger because the ball is being kicked at an angle greater than 45 degrees from horizontal.)
4. Divide your 22[m] distance from the goal by the x-component of the ball's velocity to get the time it takes to reach the goal post. 22[m]/8.654[m/s] = 2.542[s]
Step 2: Find the y-coordinate of the ball at time = 2.542[s]
1. Use the formula y_final = 0.5*y_acceleration*t^2 + y_velocity_initial*t + y_position_initial
2. Substitute values to get y_f = 0.5*-9.8[m/s^2]*(2.542[s])^2 + 14.633[m/s]*2.542[s] + 0
3. Solve to obtain y_f = 5.534 [m]
4. Subtract the height of the bar to find the distance by which the ball clears the bar. 5.534[m] - 3.05[m] = 2.48[m]
Therefore, the ball clears the bar by 2.48[m] as it passes through the goal posts.
