Answer:
The chance in distance is 25 knots
Explanation:
The distance between the two particles is given by:
(1)
Since A is traveling north and B is traveling east we can say that their displacement vector are perpendicular and therefore (1) transformed as:
(2)
Taking the differential with respect to time:
(3)
where
and
are the respective given velocities of the boats. To find
and
we make use of the given position for A,
, the Pythagoras theorem and the relation between distance and velocity for a movement with constant velocity.

with this time, we know can now calculate the distance at which B is:

and applying Pythagoras:

Now substituting all the values in (3) and solving for
we get:

Answer:
c. Joints allow the roadway to expand and contract as cars put force on the bridge
Explanation:
The reasons why joints are allowed on roadway is to accommodate the contraction and expansion of the road as cars put force on them.
- Most materials used in making roadways are susceptible to expansion and contraction.
- When a measure of force is applied their length either increases or decreases depending on the type of force.
- To accommodate these changes, joints are placed in roadways
1) the weight of an object at Earth's surface is given by

, where m is the mass of the object and

is the gravitational acceleration at Earth's surface. The book in this problem has a mass of m=2.2 kg, therefore its weight is

2) On Mars, the value of the gravitational acceleration is different:

. The formula to calculate the weight of the object on Mars is still the same, but we have to use this value of g instead of the one on Earth:

3) The weight of the textbook on Venus is F=19.6 N. We already know its mass (m=2.2 kg), therefore by re-arranging the usual equation F=mg, we can find the value of the gravitational acceleration g on Venus:

4) The mass of the pair of running shoes is m=0.5 kg. Their weight is F=11.55 N, therefore we can find the value of the gravitational acceleration g on Jupiter by re-arranging the usual equation F=mg:

5) The weight of the pair of shoes of m=0.5 kg on Pluto is F=0.3 N. As in the previous step, we can calculate the strength of the gravity g on Pluto as

<span>6) On Earth, the gravity acceleration is </span>

<span>. The mass of the pair of shoes is m=0.5 kg, therefore their weight on Earth is
</span>

<span>
</span>
Explanation:
Let f is the frequency of an oscillation and T is the period of the oscillation. There exists an inverse relationship between the frequency and the time period of the oscillation. Mathematically, it is given by :

Also, 
So,

The time taken to complete one oscillation is called the period of the oscillation and the number of oscillation is called the frequency if an oscillation.