Finding Final Velocity

In summary, the conversation is about a skydiver who needs to calculate the final velocity after falling for 10.6 seconds. They have the given values for the x and y axes, as well as the vertical velocity of 100 m/s. The formula V2= V1 + a (delta t) is mentioned, but it does not give the correct answer of 130 m/s. The key is to find the resultant of the x and y components of the final velocity.
  • #1
KaseyK
8
0
This question was actually a 3 part question. I answered (a) and (b) correctly however I can't figure out how to calculate the 'final velocity of the skydiver'. Here are the givens:

x axis
v1 - 90 m/s
acceleration - zero
delta t - 10.6 seconds
delta d - 958.5 m

Y axis
v1 = 0
delta t - 10.6 seconds
acceleration = -9.8 m/s^2
delta d = 550 m

I was already asked to calculate the vertical velocity of the skydiver which was 100 m/s.

However now they want me to find the final velocity. I was thinking about using the equation:

V2= V1 + a (delta t)

When I use this equation though I don't come up with the right answer, which is supposed to be 130 m/s.

Help!
 
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  • #2
It would help if you posted the whole question as stated to you since it's not clear what the situation is. "v1 - 90"?? I'm assuming you mean "v1 = 90"?? Anyway, i'll offer this advice: if the skydiver is not falling straight down, the final velocity will have two components to it (x and y). You need to find the resultant of those two components to get the final velocity.
 
  • #3


I would recommend using the equation for displacement (Δd) in the x-axis to find the final velocity (V2). This equation is Δd = V1Δt + 1/2a(Δt)^2, where V1 is the initial velocity, a is the acceleration, and Δt is the time interval.

In this case, we know that V1 = 90 m/s, a = 0, Δt = 10.6 seconds, and Δd = 958.5 m. Plugging in these values, we get:

958.5 m = (90 m/s)(10.6 s) + 1/2(0)(10.6 s)^2

Simplifying, we get:

958.5 m = 954 m

Therefore, the final velocity in the x-axis is 954 m/s.

To find the final velocity in the y-axis, we can use the same equation, but with the values for the y-axis given in the problem.

Δd = V1Δt + 1/2a(Δt)^2

550 m = (0)(10.6 s) + 1/2(-9.8 m/s^2)(10.6 s)^2

Simplifying, we get:

550 m = -518.6 m

Therefore, the final velocity in the y-axis is -518.6 m/s.

To find the overall final velocity, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the final velocity and the other two sides are the velocities in the x-axis and y-axis.

Using the values we found, we get:

(V2)^2 = (954 m/s)^2 + (-518.6 m/s)^2

Simplifying, we get:

(V2)^2 = 909,780 m^2/s^2 + 269,336 m^2/s^2

Therefore, the final velocity is:

V2 = √(909,780 m^2/s^2 + 269,336 m^2/s^2)

V2 = √1,179,116 m^2/s^2

V2 = 1,
 

1. How do you calculate final velocity?

Final velocity can be calculated by adding the initial velocity to the product of acceleration and time. The formula for final velocity is Vf = Vi + at, where Vf is final velocity, Vi is initial velocity, a is acceleration, and t is time.

2. What units are used to measure final velocity?

Final velocity is typically measured in meters per second (m/s) or kilometers per hour (km/h).

3. Can final velocity be negative?

Yes, final velocity can be negative if the direction of motion is opposite to the initial direction. For example, if an object is thrown upwards, its final velocity at the highest point will be negative as it starts to fall back down.

4. How does air resistance affect final velocity?

Air resistance can decrease the final velocity of an object by applying a force in the opposite direction of motion. This is why objects with greater surface area experience more air resistance and have a lower final velocity.

5. What is the difference between final velocity and average velocity?

Final velocity refers to the instantaneous velocity of an object at a specific point in time, while average velocity is the overall velocity of an object over a certain period of time. Average velocity takes into account the changes in velocity that occur during the motion, while final velocity only represents the velocity at the end of the motion.

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