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BaLLatris [955]

3 years ago

5

Fran works due north of home. Her husband Ben works due east. They leave for work at the same time. By the time Fran is 7 miles

from home, the distance between them is one mile more than Ben's distance from home. How far from home is Ben?

1 answer:

almond37 [142]3 years ago

3 0

Answer:24 m

Explanation:

Given

Distance of Fran from home is 7 miles

Distance between Ben and Fran is 1 mile more than the distance of ben from home

let distance of ben from home is x miles

therefore distance between ben and Fran is x+1 miles

using Pythagoras

$7^2+x^2=(x+1)^2$

$49+x^2=x^2+1+2x$

$48=2 x$

$x=24$

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a) See graph in attachment

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Explanation:

a)

For this part, find in attachment the diagram representing this situation.

Since we are not given any particular direction for the motion, we choose the x-direction as the direction of motion of the boat.

Then we have the following:

- The initial position of the boat is $x_i = 0$ , the origin

- The final position of the boat is $x_f = 200 m$

- The initial velocity of the boat is $v_i = 20.0 m/s$

- The final velocity of the boat is $v_f = 30.0 m/s$

Note that the arrow representing the final velocity is longer than that of the initial velocity, since the final velocity is larger.

b)

The motion of the speed boat is a uniformly accelerated motion (motion at constant acceleration), therefore we can use one of the suvat equations. In this particular problem, we know the following quantities:

$v_i = 20.0 m/s$ , the initial velocity

$v_f = 30.0 m/s$ , the final velocity

$s = x_f - x_i = 200 m$ , the displacement of the boat

Therefore, the equation that best can be use to find the acceleration is

$v_f^2 - v_i^2 = 2as$

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c)

Now we have to solve the equation

$v_f^2 - v_i^2 = 2as$

In order to find the acceleration.

This can be done by dividing both terms by $2s$ : this way, we find

$\frac{v_f^2-v_i^2}{2s}=\frac{2as}{2s}$

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