SOLUTION: A golfer on a level fairway hits a ball at an angle of 43° to the horizontal that travels 89 yd before striking the ground. He then hits another ball from the same spot with the s

Question 1205870: A golfer on a level fairway hits a ball at an angle of 43° to the horizontal that travels 89 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 89 yd. At what angle was the second ball hit? (Neglect air resistance.)

Answer by ikleyn(52818) (Show Source): You can put this solution on YOUR website!
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A golfer on a level fairway hits a ball at an angle of 43° to the horizontal that travels
89 yd before striking the ground. He then hits another ball from the same spot with the same speed,
but at a different angle. This ball also travels 89 yd.
At what angle was the second ball hit? (Neglect air resistance.)
~~~~~~~~~~~~~~~~~~~~~~~~

If a projectile is launched at an angle of  to the horizontal surface at the speed
which magnitude is V, then the distance, where it will strikes the ground is

    D = .


where "g" is the gravity acceleration at the Earth surface. 


For this formula, look into any textbook on Physics, or this web-site

https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/4-3-projectile-motion/


In our problem, two projectiles have the same starting speed V and the same horizontal
distance D, but have different launching angles  and  to the horizontal.


So, we can write this equation

     = .


Cancel common factors V in both sides. Also, cancel the denominators.  You will get

     = .


It implies

     = ,

or

     = .


Thus angles  and   are complementary.


Since in this problem one angle is 43°, hence the other angle is  90° - 43° = 47°.


ANSWER.  The other angle is 47° , complementary to the first angle of 43°.

Solved.

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