3. A boat travelling at 15 m s–1 crosses a river 100 m wide with parallel banks (Fig. 2.3). If the river current is 5 m s–1, calculate the time taken to cross the river and how far downstream the boat travels in this time. What is the displacement of the boat when it reaches the other side?
river bank
Time to cross river = d ÷ v = (width of river) ÷ (velocity of boat) = 100 ÷ 15 = 6 2
__ 3 s
Distance travelled downstream = river current velocity × time = 5 × 6 2
__ 3 = 33 1
downstream =
= 105.41 m diagonally downstream √ river bank FIG. 2.3 You may now complete Exercise 2A (page 19). Measuring velocity
To measure velocity, you need to measure displacement and time. To do this, you might use a metre rule and a stopwatch. However, this would result in a lot of errors as you are trying to measure two things at once. Instead, to measure velocity more accurately, you can use:
• a ticker timer and tape • a scaler timer and light gates.
Ticker timer and tape
A ticker timer (Fig. 2.4) has a small hammer that strikes 50 times a second (it is connected to an a.c. 50 Hz supply).
The tape is a narrow strip of paper that can be attached to an object and passed through the ticker timer. As the object moves, the tape is pulled through the timer. The hammer in the timer strikes the tape every 1 tape.
___ 50 second. Each time the paper is struck, a dot is left on the ticker
When you examine the tape, you will see the type of pattern shown in Fig. 2.5.
FIG. 2.4 A ticker timer and tape ticker timer ticker tape
