Rina's two walks met at a right angle. Kofi's hike does not: he walks 50 m east, then 30 m on a trail aimed 60° north of east.
How do we find the resultant of two displacements that meet at any angle?
First, two words for the ends of an arrow. A vector arrow has a tail, where it starts, and a tip, where the arrowhead sits.
To add two vectors, draw the second arrow so its tail starts at the first arrow's tip. Drawing arrows this way is called tip-to-tail.
Alba adds two velocity arrows in a tip-to-tail drawing. Where does she draw the second arrow's tail?
In a finished tip-to-tail drawing, where does the resultant arrow run?
To get numbers out, draw to scale. Choose a scale: 1 cm for every 10 m. Draw Kofi's first leg: an arrow 5 cm long, pointing east. From that arrow's tip, draw the second leg: an arrow 3 cm long, aimed 60° north of east. A protractor sets the 60° angle.
Draw the resultant from the first arrow's tail to the second arrow's tip. Measure the resultant with a ruler: 7.0 cm. At 10 m per centimeter, its magnitude is 70 m. Measure its direction with a protractor: the resultant sits about 22° north of east. So Kofi finishes 70 m from his start, aimed about 22° north of east.
A tip-to-tail drawing uses 1 cm for every 5 m/s. The measured resultant is 6.4 cm. Enter the resultant's magnitude in m/s.
Two velocities act together on a glider: 10 m/s east and 6 m/s aimed 60° north of east. Use a tip-to-tail scale drawing to find the resultant velocity.
Choose a scale:
1 cm for every 4 m/s
Draw the construction:
the first velocity: an arrow 2.5 cm long, pointing east
from its tip, the second velocity: an arrow 1.5 cm long, aimed 60° north of east
the resultant from the first arrow's tail to the second arrow's tip
Measure the resultant:
3.5 cm long, about 22° north of east
Convert the measurement with the scale:
magnitude = 3.5 × 4 = 14
The resultant velocity is 14 m/s, about 22° north of east.
A treasure-hunt clue says: walk 60 m east, then 60 m aimed 60° north of west. Use a tip-to-tail scale drawing at 1 cm per 10 m to find the resultant displacement.
Draw the construction:
the first leg: an arrow 6 cm long, pointing east
from its tip, the second leg: an arrow 6 cm long, aimed 60° north of west
the resultant from the first arrow's tail to the second arrow's tip
Measure the resultant:
6.0 cm long, at 60° north of east
Convert the measurement with the scale:
magnitude = 6.0 × 10 = 60
The resultant displacement is 60 m, aimed 60° north of east: the same size as each leg, between their directions.
Rina adds two displacements in a tip-to-tail scale drawing at 1 cm for every 25 m. The measured resultant is 5.2 cm. Enter the resultant's magnitude in m.
Kofi has drawn an arrow 4.0 cm east and, from its tip, an arrow 2.5 cm aimed 45° north of east. Which arrow completes the addition?
Alba's scale drawing shows a 120 m displacement as an arrow 6.0 cm long. How many meters does each centimeter stand for? Enter the number.