What Speed Does the Athlete Land in Long Jump?

In summary, the conversation discusses a problem involving a high school athlete performing a long jump at a 25 degree angle and landing 8.8m from the launching point. The question is asking for the speed at which the athlete lands, assuming the launching and landing points are at the same height. The suggested solution involves using the range formula and solving for the initial velocity.
  • #1
zman2011
7
0

Homework Statement


During a high school track meet, an athlete performing the long jump runs and leaps at an angle of 25 degrees and lands in a sand pit 8.8 m from his launching point. If the launch point and landing point are at the same height, y=0m, with what apeed does the athlete land?



Homework Equations





The Attempt at a Solution


Im completely stumped. any help would be appreciated.
 
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  • #2
Are you familiar with the range formula?
 
  • #3
no i am not.
 
  • #4
can anyone tell me what the range formula is?
 
  • #5
R = ((v0)2 sin(2[tex]\theta[/tex]0)) / g

Rearranging this formula and solving for v0 will give you the initial velocity. You can figure out the final velocity from there.
 
  • #6
well then how do i find initial velocity to put it in.
 
  • #7
i didnt see the second part of that. sorry. thank you
 
  • #8
im having trouble with this. i keep getting initial velocity as a decimal
 
  • #9
Maybe you aren't substituting/manipulating properly.

[tex] x = \frac{v_o^2sin2\theta}{g}[/tex]
[tex]v_o=\sqrt{\frac{xg}{sin2\theta}}[/tex]
 

Related to What Speed Does the Athlete Land in Long Jump?

1. What is projectile motion in the context of long jump?

Projectile motion refers to the curved path that an object takes when it is thrown or launched into the air. In the context of long jump, it is the trajectory of the athlete's body as they jump and travel through the air.

2. What factors affect the trajectory of a long jump?

The trajectory of a long jump is affected by several factors, including the initial speed and angle at which the athlete takes off, the force of gravity, air resistance, and the height and distance of the landing pit.

3. How does the angle of takeoff affect the distance of a long jump?

The angle of takeoff plays a crucial role in determining the distance of a long jump. A lower angle of takeoff results in a flatter trajectory and a shorter jump, while a higher angle of takeoff can result in a longer jump.

4. What is the optimal angle for a long jump?

The optimal angle for a long jump varies depending on factors such as the athlete's speed, strength, and technique. Generally, a takeoff angle of around 20-25 degrees is considered optimal for achieving maximum distance.

5. How does air resistance impact the long jump?

Air resistance, also known as drag, can significantly impact the trajectory and distance of a long jump. The higher the air resistance, the more it can slow down the athlete's movement through the air and reduce the distance of their jump.

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