Magnitude of the Initial Velocity

In summary, a tennis ball rolled off a flat roof with a height of 65m and hit the ground at a point 418m away from the edge of the roof. The ball was in the air for 3.64 seconds and the magnitude of its initial velocity can be calculated by finding the vector sum of its horizontal and vertical components, assuming no air resistance.
  • #1
Rose1996
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Homework Statement


A flat roof has a height of 65m above the ground. A tennis ball rolls off the edge of the roof and hits the ground at a point 418m horizontally from the edge of the roof.
A.) How much time is the ball in the air?
B.) What is the magnitude of the initial velocity?[/B]2. The attempt at a solution
I'm fairly positive that the answer to A is 3.64 seconds, but I'm having trouble understanding how to get the magnitude of the initial velocity and what it is exactly.
 
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  • #2
The velocity has horizontal and vertical components. Assuming we are to ignore air resistance (the problem doesn't say, but that is usually assumed in these simple problems, where not stated otherwise), the horizontal component won't change while the vertical component will.

So if you have the time the ball is in the air and the horizontal distance traveled you can get the horizontal velocity by a simple division. The initial velocity will be the vector sum of that plus the initial vertical velocity.
 
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Likes Rose1996
  • #3
Okay, I think I get it now. Thank you so much!
 

1. What is the definition of magnitude of the initial velocity?

The magnitude of the initial velocity refers to the size or amount of the initial velocity vector, without taking into account its direction.

2. How is the magnitude of the initial velocity measured?

The magnitude of the initial velocity can be measured using various units such as meters per second (m/s) or kilometers per hour (km/h). It can also be calculated using the formula magnitude = √(x^2 + y^2), where x and y are the horizontal and vertical components of the initial velocity.

3. What is the relationship between magnitude of the initial velocity and acceleration?

The magnitude of the initial velocity and acceleration are related in that they both affect the overall motion of an object. When the magnitude of the initial velocity increases, the acceleration also increases, resulting in a faster change in velocity. On the other hand, a decrease in the magnitude of the initial velocity leads to a decrease in acceleration and a slower change in velocity.

4. How does the angle of the initial velocity affect its magnitude?

The angle of the initial velocity affects its magnitude by determining the x and y components of the velocity vector. The magnitude of the initial velocity can be calculated using the Pythagorean theorem, where the x and y components are the horizontal and vertical sides of the triangle formed by the initial velocity vector.

5. Can the magnitude of the initial velocity be negative?

Yes, the magnitude of the initial velocity can be negative if the object is moving in the opposite direction of the chosen coordinate system. However, the magnitude itself is always a positive value, so the negative sign only indicates the direction of the initial velocity vector.

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