Motion in One Dimension

In summary, Heather and Jerry are standing on a 46 m high bridge and simultaneously throw rocks downwards and upwards with a speed of 30 m/s each. The problem requires finding the time it takes for both rocks to hit the water, which can be solved using a kinematic equation with known values of initial velocity, displacement, and acceleration.
  • #1
mcryder16
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Homework Statement



Heather and Jerry are standing on a bridge 46 m above a river. Heather throws a rock straight down with a speed of 30 m/s. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. How much time elapses between the first splash and the second splash?

Homework Equations



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The Attempt at a Solution

 
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  • #2
Solve for the time it takes both rocks to hit the water under a constant gravitational acceleration. You know initial velocity, displacement, and acceleration. All that you need is time. So find the best kinematic equation for your problem.
 
  • #3


To find the time elapsed between the first and second splash, we can use the equation t = (2d/g)^(1/2), where t is the time, d is the distance, and g is the acceleration due to gravity (9.8 m/s^2).

In this case, d = 46 m, since both rocks are thrown from the same height. Plugging in the values, we get t = (2*46/9.8)^(1/2) = 3.41 seconds.

Therefore, the time elapsed between the first and second splash is approximately 3.41 seconds. This is because both rocks are experiencing the same acceleration due to gravity, regardless of the direction in which they are thrown. This is a basic example of motion in one dimension, where only one variable (in this case, time) is changing while all other factors remain constant. By using the appropriate equation and plugging in the given values, we can accurately calculate the time elapsed between the two splashes.
 

1. What is motion in one dimension?

Motion in one dimension refers to the movement of an object along a straight line or path, without any change in direction. It is also known as linear motion.

2. What are some examples of motion in one dimension?

Some examples of motion in one dimension include a car moving along a straight road, a ball rolling down a ramp, and a person walking in a straight line.

3. What is the difference between speed and velocity in one dimension?

Speed is a measure of how fast an object is moving, while velocity is a measure of both speed and direction. In one dimension, speed and velocity are often used interchangeably since there is no change in direction.

4. What is the formula for calculating average speed in one dimension?

The formula for calculating average speed in one dimension is: speed = distance/time. This means that the distance an object travels divided by the time it takes to travel that distance will give its average speed.

5. How does acceleration affect motion in one dimension?

Acceleration is the rate at which an object's velocity changes. In one dimension, if an object has a constant acceleration, it will either speed up or slow down in a straight line. If the acceleration is zero, the object will continue to move at a constant speed.

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