Question

A projectile is launched with the velocity of 100 meters/second and at an angle 45° from horizontal. If the projectile's hang time is 14.43 seconds, what is its range?

Answer 1

Decompose the launch vector into x and y components by multiplying the magnitude by cos 45 deg and sin 45 deg respectively. The x component multiplied by 14.43 seconds should give the range.

Answer 2

That's correct but there's no need to even calculate the y component of the velocity.

You could also consider this a special case in that the angle is exactly 45 degrees so the x and y components of the velocity will be equal:\[sin(45)=cos(45)\]At any rate you end up with:\[(100m/s)(cos45)(14.43s)=?\]