Confused about THIS pHYSIcs question...

[shushumiga]

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Here it is...
Two balls having the same mass are shot from the same point with the same initial speed at the same time, but at different angles to the horizontal. Which of the following statements must be true:
a) The ball launched at the larger angle hits the ground first.
b) The ball launched at the smaller angle hits the ground first.
c) The two balls hit the ground at the same time.
d) The ball launched ar the larger angle always has more total mechanical energy.

I picked a) thinking that we are dealing with the x direction not y and since the x and y are independent of each other the time in the x direction will depens on vcosQ not vsinQ. I also picked angles of Q=30 and Q=45 and I know that it takes longer for an object to hit the ground launched at 30 degrees...
The right answer is actually b)....
WHY????

 

[solitarius]

Okay, the 30 vs. 45 degree thing is about finding the optimal range, not the time in the air.

time in air = 2 * (v_oy/g); in other words, time in air is only dependent on the initial vertical speed (v_oy). If it's a projectile with no friction, gravity is the only vertical force acting on it. So time in air will only be dependent on v_y and g through the equation v_y = v_oy + a*t.

 

[ClemsonFirst]

Also, think about it in terms of air time. The higher an object is at its point of zero vertical velocity, the longer it will take to hit the ground. So, an angle of 90 should be the longest flight time and 0 should be the shortest. So, 45 degrees will shoot the ball higher than 30. This will make the 45 degree ball have a zero velocity at a higher point from the ground than the 30 degree.

You should have thought of it in the y direction and not the x since gravity acts in the y.

On a side not, 45 is the optimum angle for longest distance in the x direction. Just an additional note.