Velocity of the bungee jumper

In summary, Lola goes bungee jumping from a bridge that is 100 m above a river. Her bungee cord has an unstretched length of 50 m and a spring constant k=700N/m. Using the equation V=√(k/m)(A)^2, Lola's speed when she just starts to stretch the cord is 197.20m/s. The second part of the question is irrelevant as the spring is not being stretched yet.
  • #1
tink123
4
0
Lola goes bungee jumping. She leaps from a bridge that is 100 m above a river. Her bungee cord has an unstretched length of 50 m and a spring constant k=700N/m. lola has a mass of 45 kg. How fast is she falling when she just starts to stretch the cord? How long does it take for Lola to reach this point.

I used the equation V=√(k/m)(A)^2 and I got

V=√(700N/m/45kg)(50m)^2)=197.20m/s

I was wondering If I used the right equation b/c the answer seems awfully high.

The second part of the question i don't know which equation to use.
Thanks
 
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  • #2
Just ignore the spring, because it is not being stretched yet. She's just plain old falling.
 
  • #3


I can confirm that you have used the correct equation to calculate the velocity of Lola when she just starts to stretch the bungee cord. However, the answer you have obtained is not correct. The equation you have used is for calculating the final velocity of an object undergoing simple harmonic motion, and it does not account for the effects of gravity and air resistance.

To accurately calculate Lola's velocity, we need to use the equations of motion for a falling object under the influence of gravity. The initial velocity of Lola is zero, as she is at rest before she jumps. The acceleration due to gravity is 9.8 m/s^2 and her displacement is 50 m (the unstretched length of the bungee cord).

Using the equation V^2 = u^2 + 2as, where V is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we can calculate that Lola's final velocity is approximately 31.3 m/s.

As for the second part of the question, we can use the equation t = √(2s/a) to calculate the time it takes for Lola to reach the point where the bungee cord starts to stretch. Plugging in the values, we get t = √(2(50m)/(9.8 m/s^2)) = 3.19 seconds.

It is important to note that these calculations assume ideal conditions and do not take into account factors such as air resistance and the elasticity of the bungee cord. In reality, Lola's velocity may be slightly lower and the time it takes for her to reach the point where the bungee cord starts to stretch may vary.
 

1. What is the velocity of the bungee jumper at the lowest point?

The velocity of the bungee jumper at the lowest point depends on several factors such as the length of the bungee cord, the weight of the jumper, and the force of gravity. In general, the velocity will be at its maximum when the bungee cord is fully extended, and it will decrease as the jumper is pulled back up.

2. How does air resistance affect the velocity of the bungee jumper?

Air resistance, also known as drag, can have a significant impact on the velocity of the bungee jumper. As the jumper falls, they will experience an upward force from the air pushing against them, which will slow them down. The amount of air resistance will depend on the surface area of the jumper and their position in the air.

3. Can the velocity of the bungee jumper be calculated?

Yes, the velocity of the bungee jumper can be calculated using the laws of physics. By taking into account the weight of the jumper, the length of the bungee cord, and the force of gravity, the velocity at different points in the jump can be determined using mathematical equations.

4. What is the relationship between the velocity and acceleration of the bungee jumper?

The velocity and acceleration of the bungee jumper are directly related. As the bungee cord stretches and the jumper falls, their velocity increases. At the same time, the acceleration due to gravity is acting on the jumper, causing them to speed up. As the cord recoils and the jumper is pulled back up, their velocity decreases, and their acceleration also decreases.

5. How does the height of the bungee jump affect the velocity of the bungee jumper?

The height of the bungee jump can have a significant impact on the velocity of the bungee jumper. A higher jump will result in a faster velocity as the jumper has more time to accelerate before reaching the lowest point. However, a higher jump also means a longer bungee cord, which can affect the velocity and acceleration of the jumper due to increased air resistance and the elasticity of the cord.

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