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Question

Answer 1

(3)

Step 1 :

Let the rocket is fired from the point .

A person is standing at point .

After seconds, rocket is at point .

Let the distance traveled by the rocket is .

Let the distance between rocket fired point to person is .

Let distance between the person and rocket after seconds .

Step 2 :

The speed rocket is .

Find distance traveled by rocket after .

Substitute , in the distance formula.

.

Distance traveled by rocket is .

Distance between rocket fired point to person is .

Apply Pythagorean theorem to the figure and Solve .

.

Distance between rocket fired after to person is 460.97 ft.

Comments

contd...

Step 3 :

Find rate of change of distance between the rocket and the person after .

Pythagoras theorem : .

Differentiate on each side with respect to .

Since person is not moving, .

Substitute , and in the above equation.

Rate of change of distance between the person and the rocket is .

Solution :

Rate of change of distance between the person and the rocket is .

Answer 2

(4)

Step 1 :

Two bikes start moving from the same point.

Let the starting point be .

After seconds, the first bike is at point .

After seconds, the second bike is at point .

Let the distance traveled by the first bike rider is .

Let the distance traveled by the second bike rider is .

Let the distance between two bike riders be .

Step 2 :

The speed of the first bike is .

The speed of the second bike is .

Time taken by the second rider to reach the point is .

The first bike rider starts early than the second bike rider, so the time taken by first bike rider to reach the point is .

Find distance traveled by each bike rider.

Distance traveled by first bike rider is .

Distance traveled by second bike rider is .

Find distance between two bike riders.

Apply Pythagorean theorem to the figure and Solve .

The distance between two riders is .

Comments

contd...

Step 3 :

Find rate of change of distance between the two bike riders.

Pythagoras theorem : .

Differentiate on each side with respect to .

Substitute , , , and in above equation.

Rate of change of distance between the two bike riders is .

Solution :

Rate of change of distance between the two bike riders is .