Calculating displacement, distance traveled, and max height

In summary, displacement can be calculated by subtracting the initial position from the final position and takes into account both magnitude and direction. It differs from distance traveled in that it considers the shortest path between positions. The maximum height in a displacement-time graph can be found by looking at the highest point on the y-axis and its corresponding time on the x-axis. Displacement can be positive, negative, or zero depending on the direction of motion. Mathematically, displacement can be represented as d = xf - xi or as the integral of velocity over time.
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Hi I need help solving this problem. Thank you.

1. Homework Statement [/b]

Given:
assume g = 9.81 m/s2, and friction can be ignored.

A ball is thrown into the air at speed 43 m/s, at an angle of 53.7 o to the ground. The ball lands at the same elevation as it was thrown.

a) Find the time it took to hit the ground in seconds

b) Find the horizontal distance the ball traveled in meters

c) find the maximum height the ball reached in meters
 
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https://www.physicsforums.com/showthread.php?t=94383
 

1. How do you calculate displacement?

Displacement can be calculated by subtracting the initial position from the final position. It is a vector quantity that takes into account both magnitude and direction.

2. What is the difference between displacement and distance traveled?

The main difference between displacement and distance traveled is that displacement takes into account the shortest path between the initial and final positions, while distance traveled is the total path length traveled regardless of direction.

3. How do you find the maximum height in a displacement-time graph?

The maximum height in a displacement-time graph can be found by looking at the highest point on the y-axis (displacement) and its corresponding time on the x-axis. This represents the highest position reached by the object.

4. Is displacement always positive?

No, displacement can be positive, negative, or zero. It depends on the direction of the object's motion relative to its initial position. Positive displacement indicates motion in the positive direction, negative displacement indicates motion in the negative direction, and zero displacement indicates no motion.

5. How can displacement be represented mathematically?

Displacement can be represented as d = xf - xi, where d is displacement, xf is the final position, and xi is the initial position. It can also be represented as the integral of velocity over time, ∫v(t)dt.

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