Question concerning initial velocity

In summary, the formula for finding the take-off speed in a long jump is distance=V(initial)*sin^2(theta)/g. However, this formula may lead to incorrect answers if there are mistakes in the algebra. The correct formula to use is Distance = V0^2sin2θ/g. By taking the vertical component first and finding the total time taken, and then taking the horizontal component of the velocity and multiplying by time, the correct answer can be obtained. It is important to be careful and organized when using algebra to avoid simple mistakes.
  • #1
Casimi
11
0

Homework Statement



An athlete executing a long jump leaves the ground at a 31.6° angle and travels 7.78 m. What was the take-off speed?

I have tried to solve this question but somehow keep arriving at the wrong answer. The formula that I derived is :

distance=V(initial)*sin^2(theta)/g

Where am I going wrong here? Any help would be appreciated.
 
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  • #2
Are you computing

distance=V0sin2θ/g

OR

Distance = V02sin2θ/g?

The second one is the one should use.
 
  • #3
It seems as if I derived the wrong formula via a mistake in my algebra.

Thank you so much!
 
  • #4
i get a different formula for it.

First take the vertical component, and find the total time taken. Now take the horizontal component of the velocity and multiply by time to find the expression for distance(range)

Substitute and get your answerEDIT: rock.freak answered first, i guess...
 
  • #5
It seems like I should take more time to organize my thoughts and perform my algebra correctly. Simple mistakes are always my downfall!
 

Related to Question concerning initial velocity

1. What is initial velocity?

Initial velocity, also known as initial speed, is the velocity of an object at the beginning of its motion. It is the rate at which an object is moving in a specific direction at the start of its journey.

2. How is initial velocity different from final velocity?

Initial velocity is the velocity of an object at the beginning of its motion, while final velocity is the velocity of an object at the end of its motion. Final velocity takes into account any changes in speed and direction that may have occurred during the object's journey.

3. What factors can affect the initial velocity of an object?

The initial velocity of an object can be affected by several factors, including the force applied to the object, the angle at which the force is applied, and the mass and shape of the object. External factors such as friction and air resistance can also impact the initial velocity.

4. How is initial velocity calculated?

The initial velocity of an object can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. If no acceleration is present, then the initial velocity can be calculated using the equation v = d/t, where d is the distance traveled and t is the time.

5. Why is initial velocity important in physics?

Initial velocity is important in physics because it helps us understand the motion of objects and how they behave in different situations. It is also a key component in calculating other important quantities such as acceleration, force, and momentum. Without considering initial velocity, our understanding of the laws of motion would be incomplete.

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