What is the height of the football at the end of its trajectory according to question 1?

Question

1. A football is thrown in the air and then blown to the right by the wind. The thrower lifts it 20 feet directly into the air before it is carried 10 feet the right at a 45 degree angle. Later, the ball is carried 40 feet at an angle of 30 degrees.

1.  What is the height of the football at the end of its trajectory?

a.      70 ft

b.      8000 ft

c.      20 feet + 5 √2

d.      5 (√2) + 20 (√3) + 20 ft

e. 2.5 (√2) + 2 (√3)

Answer 1

The problem isn't worded very well and that may be giving you issues. If I were to follow the wording, I would draw a sketch like this:

however, this results in a height of 50 feet which is not one of the answers. Therefore, they must mean something else.

My best guess its that in step 2, the hypotenuse must be meant to be the 10 foot length (making the height 5√2) and in step 3, the angle must be off the vertical, making the height 20√3. That results in answer d.

My suggestion, ask the writer of the question what they meant by their wording.

Answer 2

Here is the video explanation, folks! Please reach out should you have any questions. A big thank you to Mark M for pointing out, we are measuring the angles from the vertical component. Hopefully, that is shown better in the graph, but please reach out should you need any more clarification.

Above all, try to use this as an exemplar of solving with logic and understanding of the mind rather than pure math concepts that might slip our mind on test day! It could make the difference.