having a discussion about what answer is right to this problem

Question

You and a friend each kick a football with an initial speed of 49 feet per sec,  Your kick is project at an angle of 45 degrees and your friend's kick is projects at an angle of 60 degrees.  About how much farther will your football travel than your friend's football?

2 answers:

~10 ft

~1.2 times farther

 

?

responses are both are correct

10ft not correct because no time was given

Answer 1

The maximum horizontal travel distance may be computed by the range equation

 

R = v₀²sin(2θ) / g

 

R₁ = your range = v₀²sin[2(45°)] / g

 

R₂ = friend's range = v₀²sin[2(60°)] / g

 

R₁/R₂ = sin90° / sin120° ≅ 1.1547

 

Your range is about 1.1547 times your friend's range, which you can round down to 1.2 times farther.  Note the answer does not depend on the time.