# Velocity

## 012 Resultant of two velocity vectors

**Problem 012**

Find the resultant vector of vectors **A** and **B** shown in Fig. P-012.

## 37-38 How fast a ship leaving from its starting point

## 33-34 Time Rates: A car traveling east and airplane traveling north

**Problem 33**

From a car traveling east at 40 miles per hour, an airplane traveling horizontally north at 100 miles per hour is visible 1 mile east, 2 miles south, and 2 miles up. Find when this two will be nearest together.

## 30 - Two trains in perpendicular railroad tracks

**Problem 30**

Two railroad tracks intersect at right angles, at noon there is a train on each track approaching the crossing at 40 mi/hr, one being 100 mi, the other 200 mi distant. Find (a) when they will be nearest together, and (b) what will be their minimum distance apart.

## 22-24 One car from a city starts north, another car from nearby city starts east

**Problem 22**

One city C, is 30 miles north and 35 miles east from another city, D. At noon, a car starts north from C at 40 miles per hour, at 12:10 PM, another car starts east from D at 60 miles per hour. Find when the cars will be nearest together.

## 19-21 Two cars driving in parallel roads

**Problem 19**

One city A, is 30 mi north and 55 mi east of another city, B. At noon, a car starts west from A at 40 mi/hr, at 12:10 PM, another car starts east from B at 60 mi/hr. Find, in two ways, when the cars will be nearest together.

## 11-12 Two trains; one going to east, and the other is heading north

**Problem 11**

A train starting at noon, travels north at 40 miles per hour. Another train starting from the same point at 2 PM travels east at 50 miles per hour. Find, to the nearest mile per hour, how fast the two trains are separating at 3 PM.

## Time Rates | Applications

**Time Rates**

If a quantity x is a function of time t, the time rate of change of x is given by dx/dt.

When two or more quantities, all functions of t, are related by an equation, the relation between their rates of change may be obtained by differentiating both sides of the equation with respect to t.