physic - projectile

Question

Which of the following is INCORRECT? (assume a constant take-off velocity)


a. At a take-off angle of 10o and 75o, the distance traveled is similar but the time is much longer for 75o.
b. At a take-off angle of 45o and 75o, the distance traveled is double in a similar time for 45o
c. At a take-off angle of 60o and 75o, the distance traveled is about 13 m greater in a similar time for 60o
d. At a take-off angle of 10o and 80o, the short distance is traveled in a shorter time at 80o
e. At a take-off angle of 50o and 35o, the distance is similar but the maximal height to the parabola is greater at 50o

Answer 1

time to reach peak.  Final velocity = 0.

 

V_f = V₀ sin x -gt

 

0 = V₀sin X -gt

 

t = (v₀sinx )/g  Time to hit ground = 2t = (2vsinx)/g

                                                    

 

Distance traveled = vx * delta t =   (2v₀cosx vsinx)/g  =  (v₀²sin2X)/g

                                                 

 

So angles where sin2X are equal travel about the same distance   sin 2*50 = sin 2*35 are similar, but with a larger initial vertical velocity 2v₀sin x the time required at 75 is longer.   

 

10 and 80 degrees also result in the exactly same distance traveled, but the problem incorrectly states that the time is traveled at 80 is shorter.   It is instead longer.