When running a half marathon (13.1 miles), it took Kevin 8 minutes to run from mile marker 1 to mile marker 2, and 18 minutes to
2 answers:
Answer:
It took Kevin 26 minutes to run from markers 1 to 4
His average speed from mile markers 1 to 4 is 0.154 miles/minute
Kevin must run by average speed 0.1 miles/minute to finish the race
Explanation:
Lets explain how to solve the problem
A half marathon 13.1 miles
Kevin took 8 minutes to run from mile marker 1 to mile marker 2 and
18 minutes to run from mile marker 2 to mile marker 4
→ He took 8 minutes and 18 minutes to run from marker 1 to marker 4
→ The total time of the first 4 marker = 8 + 18 = 26 minutes
<em>It took Kevin 26 minutes to run from markers 1 to 4</em>
<em></em>
Average speed is total distance divided by total time
The average speed of Kevin as he ran from mile marker 1 to mile
marker 4 is the 4 miles divides by 26 minutes
→ Average speed = 4 ÷ 26 = = 0.154 miles/minute
<em>His average speed from mile markers 1 to 4 is 0.154 miles/minute</em>
<em></em>
It took Kevin 71 minutes to pass mile marker 9
Kevin need to complete the race in 112 minutes, then what must
Kevin's average speed be as he travels from mile marker 9 to the
finish line?
The total distance of the race is 13.1 miles, he ran 9 miles
→ The remaining distance = 13.1 - 9 = 4.1 miles
He must run 4.1 miles to complete the race
The total time is 112 minutes, he used 71 minutes to run the first 9 miles
→ The remaining time = 112 - 71 = 41 minutes
He must finish the 4.1 miles in 41 minutes
→ His average speed for the last part of the race = 4.1 ÷ 41 = 0.1 mi/min
<em>Kevin must run by average speed 0.1 miles/minute to finish the race</em>
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First, you need to make certain assumptions before solving this question. Why? Because there are no information given about the direction of these forces. In such questions as above, ALWAYS make the following assumptions:
1) Take first force, say
, and assume that it is pointing towards the x-direction.
Let us take the 7N force! By keeping the above assumption in our minds, the force vector would be like:
= 
, where 
= Unit vector in the x-direction.
2) Take the second force, say
, and assume that it is making an angle 
with the first force .
Let us take the 15N force! By keeping the above assumption in our minds, the forces vector would be like:
Now from simple vector addition, we know that,
--- (A)
Where
= Resultant vector.
NOTE: In equation (A), all forces are in vector notation. Assume that there is an arrow head on top of them.
Let us find
first!
= 
=> = 
Now the magnitude of is,
|| = 
=> || = 
Since
, therefore,
=> || = 
Since || = ||, and the magnitude of the resultant force is 20N, therefore,
|| = | |
20 =
Take square on both sides,
400 =
Ans: Angle formed by the two forces, 7N and 15N, is: 53.13°
-israr
1) Take first force, say
Let us take the 7N force! By keeping the above assumption in our minds, the force vector would be like:
2) Take the second force, say
Let us take the 15N force! By keeping the above assumption in our minds, the forces vector would be like:
Now from simple vector addition, we know that,
Where
NOTE: In equation (A), all forces are in vector notation. Assume that there is an arrow head on top of them.
Let us find
=>
Now the magnitude of
|
=> |
Since
=> |
Since |
|
20 =
Take square on both sides,
400 =
Ans: Angle formed by the two forces, 7N and 15N, is: 53.13°
-israr