Question

A girl standing on top of a roof throws a stone into the air with velocity +v. She then throws a similar stone directly downwards with a velocity -v. Compare the velocities of both stones when they reach the ground.

Answer 1

Both stones thrown from the roof, one upwards with +v and the other downwards with -v, will have the same speed when they reach the ground due to gravity affecting them equally, but their velocities will be in opposite directions.

Step-by-step explanation:

Comparing Velocities of Stones Thrown Upward and Downward

When comparing the velocities of two stones, one thrown upwards and one thrown downwards from a roof with the same magnitude of velocity but opposite directions, we rely on the principles of projectile motion and gravity. If we neglect air resistance, both stones will have the same speed when they reach the ground, but their velocities will be in opposite directions. This is because gravity will accelerate both stones at the same rate (assuming the point of release is at the same height above the ground), and the initial velocity will be canceled out. In Example 2.14, a rock is thrown with an initial velocity of +13.0 m/s upwards and has a velocity of -13.0 m/s when it returns to its initial elevation on its way down. Therefore, a rock thrown downwards at -13.0 m/s will also have a velocity of -13.0 m/s at the same elevation. Consequently, both stones will have the same speed but opposite directions when they hit the ground.

Answer 2

Answer: The two stones will have different final velocity due to different distance covered ( height ) reaching the ground at different time.

Step-by-step explanation:

Throwing a stone into the air with velocity +v means she throws the stone with an upward velocity. She then throws a similar stone directly downwards with a velocity -v.

The two stones will have different final velocity due to different distance covered ( height ) reaching the ground at different time.