Understanding Vertical Motion: Time Difference Between Throwing Upward and Downward

Two Students Experiment on a Balcony

Two students are on a balcony 19.6m above the street. One student throws a ball vertically downward at 14.7 m/s. At the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down.

Finding the Time Difference

What is the difference in the time the balls spend in the air?

Final answer: 2.0 seconds

The ball thrown upwards spends 2.0 seconds more in the air compared to the ball thrown downwards.

Explanation

In this question, we first find the time it takes for each ball to hit the ground. Once we have both times, we simply subtract one from the other to get the difference.

The formula we'll use is that for motion under gravity, which is:

d = (1/2)gt^2 + vt

Where:

  • g is the acceleration due to gravity (approximately 9.8m/s^2)
  • t is time
  • v is the initial velocity
  • d is the displacement

For the first ball thrown downwards, we know d = -19.6m (because it's going downwards), v = -14.7m/s, and g = 9.8m/s^2. Substituting these into our equation and solving for t gives us t1 = 1.0 seconds.

For the second ball thrown upward, we know d = -19.6m, v = 14.7m/s, and g = 9.8m/s^2. Substituting these into our equation and solving for t gives us t2 = 3.0 seconds.

The difference in times is then simply t2 - t1 = 3.0s - 1.0s = 2.0 seconds. So the ball thrown upwards spends an extra 2.0 seconds in the air compared to the ball thrown downwards.

Question:

What is the difference in the time the balls spend in the air?

Answer:

The ball thrown upwards spends 2.0 seconds more in the air compared to the ball thrown downwards.

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