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REMARKS The angle at which the ball is thrown affects the velocity vector throughout its subsequent motion, but doesn't affect the speed at a given height. This is a consequence of the conservation of energy. QUESTION If the ball is thrown at half the given speed, then it will land: more than half as far from the building. less than half as far from the building. farther from the building than before. half as far from the building. Consider how halving the speed affects the horizontal component of velocity. How then must the time of flight change for the ball to land half the distance from the building? So consider next how the time of flight actually changes. By what factor is the time to reach zero velocity upward changed by halving the initial speed? Does the downward part of the fall now start from a higher or lower position, and how does that affect the time of downward part of the trip? Based on which times you decided were increased or decreased, how is the total time of flight affected by halving the initial speed, and how does that affect the range of the throw? PRACTICE IT Use the worked example above to help you solve this problem. A ball is thrown upward from the top of a building at an angle of 30.0° to the horizontal and with an initial speed of 21.0 m/s. The point of release is h = 42.0 m above the ground. (a) How long does it take for the ball to hit the ground?

          REMARKS The angle at which the ball is thrown affects the velocity vector throughout its subsequent motion, but doesn't affect the speed at a given height. This is a consequence of the conservation of energy.

QUESTION If the ball is thrown at half the given speed, then it will land:
more than half as far from the building.
less than half as far from the building.
farther from the building than before.
half as far from the building.

Consider how halving the speed affects the horizontal component of velocity. How then must the time of flight change for the ball to land half the distance from the building? So consider next how the time of flight actually changes. By what factor is the time to reach zero velocity upward changed by halving the initial speed? Does the downward part of the fall now start from a higher or lower position, and how does that affect the time of downward part of the trip? Based on which times you decided were increased or decreased, how is the total time of flight affected by halving the initial speed, and how does that affect the range of the throw?

PRACTICE IT
Use the worked example above to help you solve this problem. A ball is thrown upward from the top of a building at an angle of 30.0° to the horizontal and with an initial speed of 21.0 m/s. The point of release is h = 42.0 m above the ground.
(a) How long does it take for the ball to hit the ground?

REMARKS The angle at which the ball is thrown affects the velocity vector throughout its subsequent motion, but doesn't affect the speed at a given height. This is a consequence of the conservation of energy.

QUESTION If the ball is thrown at half the given speed, then it will land:
more than half as far from the building.
less than half as far from the building.
farther from the building than before.
half as far from the building.

Consider how halving the speed affects the horizontal component of velocity. How then must the time of flight change for the ball to land half the distance from the building? So consider next how the time of flight actually changes. By what factor is the time to reach zero velocity upward changed by halving the initial speed? Does the downward part of the fall now start from a higher or lower position, and how does that affect the time of downward part of the trip? Based on which times you decided were increased or decreased, how is the total time of flight affected by halving the initial speed, and how does that affect the range of the throw?

PRACTICE IT
Use the worked example above to help you solve this problem. A ball is thrown upward from the top of a building at an angle of 30.0° to the horizontal and with an initial speed of 21.0 m/s. The point of release is h = 42.0 m above the ground.
(a) How long does it take for the ball to hit the ground?

Added by Mark L.

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