Question

The four darts described below are all thrown at exactly the same time. Which will hit the ground last?

A, with an initial vertical velocity of 10 m/s and an initial horizontal velocity of 10 m/s.
B, with an initial vertical velocity of 15 m/s and an initial horizontal velocity of 0 m/s.
C, with an initial vertical velocity of 5 m/s and an initial horizontal velocity of 0 m/s.
D, with an initial vertical velocity of 5 m/s and an initial horizontal velocity of 20 m/s.

Answer 1

All four darts will hit the ground at the same time, approximately 2.04 seconds after being thrown.

The time for projectile motion is completely determined by the vertical motion. So any projectile that has an initial vertical velocity of 5 m/s and lands 20.0 m below its starting altitude will spend approximately 2.04 s in the air. Comparing the given scenarios:

1. Scenario A has an initial vertical velocity of 10 m/s and an initial horizontal velocity of 10 m/s. The projectile will take 2.04 s to hit the ground because it has a higher initial vertical velocity.
2. Scenario B has an initial vertical velocity of 15 m/s and an initial horizontal velocity of 0 m/s. The projectile will take 2.04 s to hit the ground because it has a higher initial vertical velocity.
3. Scenario C has an initial vertical velocity of 5 m/s and an initial horizontal velocity of 0 m/s. The projectile will take 2.04 s to hit the ground.
4. Scenario D has an initial vertical velocity of 5 m/s and an initial horizontal velocity of 20 m/s. The projectile will take 2.04 s to hit the ground because the horizontal component does not affect the time of flight.

Thus, all four darts will hit the ground at the same time, approximately 2.04 seconds after being thrown.