Answer:
the ball launched upward will take longer to reach the ground
Step-by-step explanation:
You want to compare the flight times of a ball that is dropped, and a ball that is thrown upward at a 40° angle.
Flight time
Neglecting air resistance, the time it takes a dropped object to reach the ground is proportional to the square root of the height from which it is dropped.
A ball launched upward at a 40° angle will reach the peak of its travel some time after it is launched. That point will be higher than the level from which it is launched. At that point, the vertical speed is zero, so the remaining flight time will be the same as that of a ball dropped from that height. (We will call this the "dropped" height.)
So, the ball launched upward will take longer to reach the ground for two reasons:
- it will reach the height equivalent to its "dropped" height some time after it was launched
- the "dropped" height will be higher than the initial height, so the flight time will be longer that of a ball dropped from the initial height.
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Additional comment
The attached graph shows the height versus time for two cases. The initial height is 10 meters in both cases.
For the ball launched upward, the speed at which it is thrown is chosen so it reaches its maximum height 1 second after it is thrown. The time it hits the ground is 1.315 seconds after the dropped ball hits the ground. This time difference includes the 1 second it took to reach the "dropped" height, and the additional 0.315 seconds required to fall from that higher starting point.