VECTORS

Film Loop: Vector Addition: Velocity of a boat

Length: 3:35 min., Black and White, No sound

In this film, a motorboat was photographed from a bridge. The operator of the boat tried to keep the throttle at a fixed setting to maintain a steady speed relative to the water. The boat heads upstream, downstream, directly across stream, and at an angle somewhat upstream so as to move straight across.

Project the film on graph paper and mark the lines along which the boat moves. It might be advisable to use the reference crosses on the markers. Then measure speeds by timing the motion through some predetermined number of squares. Repeat each measurement several times, and use the average times to calculate speeds. Express all speeds in the same unit. Why is there no need to convert the speeds to meters per second? Why is it a good idea to use a large distance between the timing marks on the graph paper?

The head-to-tail method of adding vectors is illustrated in physics texts. Since velocity is a vector with both magnitude and direction, we can study vector addition by using velocity vectors. An easy way of keeping track of the velocity vectors is by using subscripts:

vBE velocity of boat relative to earth

vBW velocity of boat relative to water

vWE velocity of water relative to earth, then

vBE = vBW + vWE

For each heading of the boat, a vector diagram can be drawn by laying off the velocities to scale.

SCENE 1: Two pieces of cardboard are dropped overboard. Time the blocks. Find the speed of the river, the magnitude of vWE.

SCENE 2: The boat heads upstream. Measure vBE,then find vBW using a vector diagram.

SCENE 3:The boat heads downstream. Measure vBE, then find vBW using a vector diagram.

SCENE 4: The boat heads across stream and drifts downward. Measure the speed of the boat and the direction of its path to determine vBE. Also measure the direction of vBW, the direction the boat points. One way to record data is to use a set of axes with the 0degrees - 180 degrees axis passing through the markers anchored in the river.

SCENE 5: The boat heads upstream at an angle, but moves across stream.

CHECKING YOUR WORK: a.) How well do the four values of the magnitude of vBWagree with each other? Can you suggest reasons for any discrepancies? b.) In part 4, you can find a calculated heading of the boat. How well does this angle agree with the observed boat heading? c.) In part 5, determine a direction for vBW. Does this angle agree with the observed boat heading?