Scalars and vectors
Grade 11 Science Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
A boat travels 5 m/s in still water. It aims upstream to land directly opposite on a river 80 m wide with a 3 m/s current. How long is the crossing, Ari?
A boat travels 13 m/s in still water. It aims upstream to land directly opposite on a river 312 m wide with a 5 m/s current. How long is the crossing, Bo?
A boat travels 10 m/s in still water. It aims upstream to land directly opposite on a river 120 m wide with a 6 m/s current. How long is the crossing, Esme?
A 0.50 kg ball moving 6 m/s east hits a wall and rebounds at 4 m/s west. The contact lasts 0.020 s. What average force does the wall exert on the ball, Jun?
- 150 N, pointing west
- 250 N, pointing east
- 250 N, pointing west
- 50 N, pointing west
Milo says two forces of equal size always add to twice that size. Agree or disagree?
- Agree: adding two equal numbers always gives double, whatever the directions, so the sum is twice that size
- Disagree: that happens only for the same direction; at right angles the sum is about 1.4 times, and opposite forces give 0
- Disagree: two equal forces always cancel, because equal sizes mean equal and opposite
- Agree: that is true unless the forces are at right angles, when they cannot add at all
Read this first
Drone positions (example data)
Time (s) East (m) North (m) 0 0 0 10 30 40 20 30 0 A drone flies straight between the readings in the table. Noah says its average velocity over the 20 s is 4.5 m/s. Does the table support the claim?
- Yes: it flew 50 m and then 40 m, which is 90 m in 20 s, so 4.5 m/s is its velocity
- No: it ends 30 m from the start, so its average velocity is 30 m/s east
- No: it ends 30 m east of the start, so the average velocity is 1.5 m/s east; 4.5 m/s is its average speed
- Yes: velocity and speed have the same size for a drone
Three tugboats pull a barge with equal 500 N forces, spaced 120° apart. Pia says the net force is 1,500 N. Agree or disagree?
- Disagree: at 120° apart the three pulls cancel, so the net force is 0 N
- Agree: three pulls of 500 N add to 1,500 N
- Disagree: the net force is 1,000 N, since two pulls cancel and one is left
- Disagree: the net force is 500 N, since just one pull counts
Car A moves at 20 m/s east and car B at 15 m/s north. What is B's velocity relative to A, Ren?
- 35 m/s, directed north of west
- 25 m/s, directed 37° north of west
- 25 m/s, directed 37° north of east
- 5 m/s, directed north
Tala must fly a plane due north over the ground. Its airspeed is 200 km/h, and a 40 km/h wind blows from the west. What heading and ground speed work?
- Head 11.5° east of north; ground speed about 196 km/h
- Head 11.5° west of north; ground speed 160 km/h
- Head 11.5° west of north; ground speed about 196 km/h
- Head due north; ground speed 200 km/h
A trip has an average speed of 8 m/s and an average velocity of 10 m/s. Can both be true, Zee?
- No: the displacement cannot be longer than the distance traveled, so the average velocity cannot be bigger
- No: speed and velocity must be equal for any trip
- Yes: velocity is a vector, so its size can be larger than the speed
- Yes: it happens when the trip is a straight line