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Suppose the ball falls 1.0000 m in 0.45173 s. Assuming the ball is not affected by air resistance, what is the precise acceleration due to gravity at this location?
Strategy
Draw a sketch.
We need to solve for acceleration . Note that in this case, displacement is downward and therefore negative, as is acceleration.
Solution
1. Identify the knowns. ; ; ; .
2. Choose the equation that allows you to solve for using the known values.
3. Substitute 0 for and rearrange the equation to solve for . Substituting 0 for yields
Solving for gives
4. Substitute known values yields
so, because with the directions we have chosen,
Discussion
The negative value for indicates that the gravitational acceleration is downward, as expected. We expect the value to be somewhere around the average value of , so makes sense. Since the data going into the calculation are relatively precise, this value for is more precise than the average value of ; it represents the local value for the acceleration due to gravity.
A chunk of ice breaks off a glacier and falls 30.0 meters before it hits the water. Assuming it falls freely (there is no air resistance), how long does it take to hit the water?
We know that initial position , final position , and . We can then use the equation to solve for . Inserting , we obtain
where we take the positive value as the physically relevant answer. Thus, it takes about 2.5 seconds for the piece of ice to hit the water.
What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down?
An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration due to gravity have the same sign on the way up as on the way down?
How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of on Earth)?
Assume air resistance is negligible unless otherwise stated.
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