How Many Meters Did You Win the Race By?

In summary, the problem involves finding the distance by which the winner won the 100.000 m dash, given their total time of 11.800 s and winning margin of .001 s. Two methods are presented, with the correct answer being .008m, but a discrepancy is found in the second method due to a typo in the given values.
  • #1
jesusu2
5
0

Homework Statement


You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by .001 s, by how many meters did you win?

Homework Equations


vavg=Δx/Δt
v=x/t

The Attempt at a Solution


I have the answer already with the method for solving it:
v=x/t = 100.00m/11.8s =8.4746m/s.
v=x/t = x=vt = 8.4746m/s(.001s)= .008m

This is the provided answer, however, I tried a different method and got ".0008m" instead, I don't know why. Here's what I did

100m/11.8s= 8.474576271 m/s (this is the average velocity of the winner)
100m/11.8001=8.474504453m/s (this is the average velocity of the loser)

I multiplied the avg velocity of the loser by 11.8, to get the position of the loser as the winner wins.
I got 99.99915255 m. I subtracted this from 100, to see by how many meters the winner won by and I got
.00084745 meters. Don't know why I got an extra 0 in my answer, can anyone please explain? Thanks!
 
Physics news on Phys.org
  • #2
jesusu2 said:

Homework Statement


You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by .001 s, by how many meters did you win?



Homework Equations


vavg=Δx/Δt
v=x/t

The Attempt at a Solution


I have the answer already with the method for solving it:
v=x/t = 100.00m/11.8s =8.4746m/s.
v=x/t = x=vt = 8.4746m/s(.001s)= .008m

This is the provided answer, however, I tried a different method and got ".0008m" instead, I don't know why. Here's what I did

100m/11.8s= 8.474576271 m/s (this is the average velocity of the winner)
100m/11.8001=8.474504453m/s (this is the average velocity of the loser)

I multiplied the avg velocity of the loser by 11.8, to get the position of the loser as the winner wins.
I got 99.99915255 m. I subtracted this from 100, to see by how many meters the winner won by and I got
.00084745 meters. Don't know why I got an extra 0 in my answer, can anyone please explain? Thanks!

The two values in red do not match. Second should be 11.801
 

Related to How Many Meters Did You Win the Race By?

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It deals with concepts such as displacement, velocity, acceleration, and time.

2. How do I approach a kinematics problem?

The first step is to identify the known and unknown quantities in the problem. Then, use the appropriate equations of kinematics to solve for the unknown quantity. It is important to pay attention to units and use the correct formula for the specific type of motion (e.g. constant velocity, constant acceleration).

3. What is the difference between displacement and distance?

Displacement is a vector quantity that refers to the change in position of an object from its initial to final position. It takes into account the direction of the motion. Distance, on the other hand, is a scalar quantity that refers to the total length of the path traveled by an object. It does not consider direction.

4. How do I calculate velocity from a position-time graph?

The slope of a position-time graph represents the velocity of an object. To calculate the velocity, choose two points on the graph and divide the change in position (y-axis) by the change in time (x-axis) between those two points.

5. Can kinematics be applied to objects moving in a curved path?

Yes, kinematics can be applied to objects moving in a curved path. In this case, the motion is described in terms of tangential velocity, centripetal acceleration, and radius of curvature. These concepts are used in circular motion and projectile motion problems.

Similar threads

Can a Tiger Outrun a Lion in a 100 Meter Dash?
    • Introductory Physics Homework Help
Replies
1
Views
1K
Who Wins the Drag Race Based on Constant Acceleration?
    • Introductory Physics Homework Help
Replies
5
Views
2K
Can the Slower Cyclist Win if the Race is Short Enough?
    • Introductory Physics Homework Help
Replies
10
Views
2K
Can a Runner Accelerate to Finish a 10,000 Meter Race in Time?
    • Introductory Physics Homework Help
Replies
4
Views
1K
Can Lance Armstrong Beat a Healthy Young Male in a Hill-Climbing Bike Race?
    • Introductory Physics Homework Help
Replies
2
Views
2K
Solving Kinematics Problem: Who Wins the Race?
    • Introductory Physics Homework Help
Replies
3
Views
1K
How Do You Solve a 1-D Motion Kinematics Problem Involving a Missile?
    • Introductory Physics Homework Help
Replies
4
Views
3K
How Long Did the Runner Accelerate to Finish the 1500m Race on Time?
    • Introductory Physics Homework Help
Replies
11
Views
2K
How Does a Sprinter's Acceleration Affect Race Time?
    • Introductory Physics Homework Help
Replies
2
Views
4K
How Do You Solve Basic Kinematics Problems in Physics?
    • Introductory Physics Homework Help
Replies
5
Views
4K

Hot Threads

Recent Insights

Back
Top