Dot Products
Cross Products
Displacement
Velocity
Acceleration
2d Motion
Projectile Motion
Uniform Circular Motion
100
Find the dot product.
hat a = 6 hat i + 4 hat j - 8 hat k
hat b = 2 hat i + 9 hat j
What is 48?
100
Find A x B.
A = i + 7j - 8k
B = 2i - 2j +k
What is - 9i - 17j - 16k?
100
You are tied to a tree by a 5m rope. You walk two full circles around the tree. This is your displacement.
What is zero?
100
You are driving at 60 miles per hour. How fast are you going in meters per second?
(hint: 1 inch = 2.54 cm)
What is 26.8 m/s?
100
The velocity equation is
v = 12 + 6t.
This is the acceleration at 32.4 seconds.
What is 6 m/s2?
100
A swimmer heads directly across a river swimming at 1.6 m/s relative to still water. She arrives at a point 40 m downstream from the point directly across the river, which is 80 m wide. Determine the speed of the current.
What is 0.8m/s?
100
A ball is launched horizontally. Its initial X velocity is 7.00 m/s. This is its x velocity after 1.30 seconds.
What is 7.00 m/s?
100
A helicopter rotor spins at 500 RPM.
Each blade is 3m long.
If a ladybug is sitting on the tip of one rotor, how fast is it going?
What is 157m/s?
200
|A| = 4.00
|B| = 3.00
The angle between is 30.0 degrees.
Find the dot product.
What is 10.4?
200
|A| = 45
|B| = 55
The angle between is 30 degrees.
Find the magnitude of the cross product.
What is 1.24x103?
200
You drive a car 200m and then get out and walk perpendicular to your path another 10.0m. This is your displacement.
What is 200m?
200
A man walks 7 km in 2 hours and 2 km in 1 hour in the same direction.
This is his average speed for the whole journey.
What is 3km/hr?
200
From rest, a car accelerated at 8 m/s2 for 10 seconds.
This is the position of the car after 10 seconds.
What is 400m?
200
A swimmer heads directly across a river swimming at 1.6 m/s relative to still water. She arrives at a point 40 m downstream from the point directly across the river, which is 80 m wide.
Determine the magnitude of the swimmer's velocity from the perspective of the shore.
What is 1.8m/s?
200
You fire a bullet out of a gun and, at the same time, drop a bullet at the same height. This is the bullet that hits the ground first.
What is neither?
200
To get he last of the ink out of a marker, you need to spin it on the end of a string. The string is 1m long. The marker travels at 16.4 m/s. This is how long the marker takes to make a full revolution (the period).
What is 0.653 seconds?
300
A = 12i - 4j + 16k
B = 4i + 32j + ?k
The dot product is zero.
Find ?
What is 5?
300
a = 12i + 4j - 3k
b = 2i
Find a x b.
What is - 6j - 8k?
300
You walk 20.0m into a building, take an elevator up 10.0m, and then walk 5.00m down a hallway perpendicular to your walk into the building. This is your displacement.
What is 22.9m?
300
A man walks 7 km in 2 hours and 2 km in 1 hour in the same direction (the positive x axis).
This is his average velocity for the whole journey.
What is 3 km/hr along the positive x axis?
300
With an initial velocity of 20 km/h, a car accelerated at 8 m/s2 for 10 seconds. This is its position after 10 seconds.
What is 456 m ?
300
A swimmer heads directly across a river swimming at 1.6 m/s relative to still water. She arrives at a point 40 m downstream from the point directly across the river, which is 80 m wide.
Determine the angle from straight that the swimmer takes across the river (i.e. if straight across is positive y, what is the angle from positive y to the swimmer's path?)
What is 27 degrees?
300
A Fort McHenry cannon on the ground fires at an angle of 12.5 degrees with an initial velocity of 60.0 m/s. This is its y-velocity when it reaches the ground.
What is -13.0 m/s?
300
You are drifting around a circle in the parking lot 15m in diameter at 5m/s. This is your centripetal acceleration.
What is 3.33 m/s2?
400
Find the dot product
hat a = -3 hat i - 8 hat k
hat b = 12 hat i - 9 hat j - 4 hat k
What is -4?
400
The magnitude of the cross product is 7.00.
|a| = 3.00
|b| = 8.00
Find the angle between.
What is 17.0 degrees?
400
An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure above.
This is the object's displacement.
What is 9 km?
400
A man walks 7 km East in 2 hours and then 2.5 km West in 1 hour.
This is the man's average velocity for the whole journey.
What is 1.5 km/hr?
400
A car accelerates uniformly from 0 to 72 km/h in 11.5 seconds. This is the acceleration of the car.
What is 1.74 m/s2?
400
A swimmer heads directly across a river swimming at 1.6 m/s relative to still water. She arrives at a point 40 m downstream from the point directly across the river, which is 80 m wide.
Determine the time it takes for the swimmer to cross the river.
What is 50s?
400
A ball is launched horizontally from 7.20m up. It travels to a distance of 70.5m from the base of its launch point. This is its initial velocity.
What is 58 m/s?
400
A rock on a string is swinging at 14m/s on the end of a 2m rope. What is the velocity if you shorten the rope suddenly to 1m? (hint: radial acceleration stays the same)
What is 9.90 m/s?
500
|A| = 12.0
|B| = -4.00
The angle between is 45.0 degrees.
Find the dot product.
What is -33.9?
500
The dot product is 90.0.
|a| = 14.0
|b| = 15.0
Find the magnitude of the cross product.
What is 190?
500
An object moves from point A to point C along the rectangle shown in the figure above.
Find the distance the object covers.
What is 8km?
500
You start walking from a point on a circular field of radius 0.5 km and 1 hour later you are at the same point.
This is your average velocity for the journey.
What is zero?
500
A car accelerates uniformly from 0 to 72 km/h in 11.5 seconds. This is its position at the end of the acceleration.
What is 115m?
500
A car enters an intersection at 20 m/s where it collides with a truck. The impact rotates the car 90° and gives it a speed of 15 m/s. Determine the magnitude of the average acceleration of the car if it was in contact with the truck for 1.25 s.
What is 20m/s2?
500
A cannon ball is shot at 60 m/s at an angle of 20° above the horizontal. This is its maximum height.
What is 21.0m?
500
A pilot cuts a tight turn of radius 200m with a speed of 100m/s. How many Gs does she experience?
(hint: 1 G is 9.8 m/s2)
What is 5.10 Gs?
600
|A| = 8.00
|B| = 4.00
The dot product is 12.0
Find the angle between.
What is 68.0 degrees?
600
Given the vectors:
A = 3i + 2j – k
B = 5i +5j
This is the cross product A×B.
What is 5i - 5j + 5k?
600
An object moves from point A to point C along the rectangle shown in the figure above.
Find the magnitude of the displacement of the object.
What is 5.83km?
600
A train travels along a straight line at a constant speed of 60 mi/h for a distance d and then another distance equal to 2d in the same direction at a constant speed of 80 mi/h.
This is the train's average speed for the whole journey.
What is 72 mi/hr?
600
An object is thrown straight down from the top of a building at a speed of 20 m/s. It hits the ground with a speed of 40 m/s.
This is the height of the building.
What is 61.2m?
600
A plane is traveling at 650 km/hr in a direction 37° east of north. Find the how far the plane travels north and east in 90 minutes.
What is 587 km E and 749 km N ?
600
You use a hose to spray your house angle of 40.0° above the horizontal. The water leaves the nozzle with a speed of 28.0 m/s. This is how far from your house you should stand away to wash the highest spot. (Water is the projectile here)
What is 38.52m?
600
In a merry-go-round moving with a speed of 3 m/s a 25-kg child is sitting 3 m from its center.
Calculate the centripetal acceleration of the child.
What is 3 m/s2?
700
Find the dot product
hat a = -6.10 hat i + 0.03 hat j - 8.00 hat k
hat b = 4.23 hat i - 5.00 hat j + 4.20 hat k
Watch your sig figs
What is 7.6?
700
x = 2i + 8j + 4k
y = 5i + 3j + 2k
Find the cross product x x y.
What is 4i + 16j - 31k?
700
An object moves along the grid through the points A, B, C, D, E, and F as shown above.
Find the distance covered by the moving object.
What is 6.5km?
700
A car travels 22 km south, 12 km west, and 14 km north in half an hour.
This is the car's average velocity for the whole journey.
What is 28.8 km/hr?
700
This is how long it takes an airplane to take off if it needs to reach a speed on the ground of 350 km/h over a distance of 600 meters (assume the plane starts from rest).
What is 12.3 seconds?
700
A seagull flying with an air speed of 10 km/h is flying north but suddenly encounters a wind of 5 km/h at 20° south of east. This is the new direction and airspeed of the seagull.
What is 9.5 km/h 30 degrees E of N ?
700
In a water balloon fight, one kid throws a balloon from a height of 1.4m at 3.00 m/s at an angle of 30 degrees. The water balloon needs to hit with a speed of 5.00 m/s or more to pop. This is what the balloon will do on landing.
What is pop?
700
A cyclist moves around a circular path with a radius of 50 m at a speed of 10 m/s.
Find the acceleration of the cyclist.
What is 2 m/s2?
800
|A| = 22.5
|B| = 9.81
The angle between is 80.0 degrees.
Find the dot product.
What is 38.3?
800
A = 2i +3j +4k
B = i + 3k
Using the cross product, find the angle between the vectors.
What is 34.7 degrees?
800
An object moves along the grid through the points A, B, C, D, E, and F as shown above.
Find the magnitude of the displacement of the object.
What is 2.5km?
800
Florence Griffith-Joyner holds the world record in women's hundred meter sprint, having completed it in 10.49 seconds. This was her average velocity.
What is 9.53 m/s?
800
This is the smallest distance, in meters, needed for an airplane touching the runway with a velocity of 360 km/h and an acceleration of -10 m/s2 to come to rest?.
What is 500m?
800
A plane heading due north with an air speed of 250 km/h is blown off course by a wind blowing at 50 km/h to the NE. This will be the ground speed and direction of the plane.
What is 288 km/h 8 degrees E of N
800
A catapult launches a flaming barrel 600m, starting at an angle of 45 degrees. This was the barrel's initial velocity. Both the catapult and the landing position are on the ground.
What is 76.6 m/s?
800
A jet plane is maneuvering in a circular path of a radius of 5.5 km at a constant speed of 2160 km/h. This is the acceleration of the plane in g's.
What is 7.35 g's?
900
Find the angle between 2i+3j+6k and -2i+2j+k.
3 sig figs.
What is 67.6 degrees?
900
a = <1,-1,2>
b = <3,-1,-1>
Find the cross product a x b.
What is 2i + 7j + 3k?
900
A plumber is trying to find where a sink is in relation to the hot water tank downstairs. He using a string to drop a washer down the pipe to the lower floor and finds it 1.4m away. When he goes to the lower floor, he finds the washer 8m down a hall and 3 m perpendicular to the hallway from the hot water tank. This is the total straight distance from the water tank to the sink.
What is 8.66m?
900
The position as a function of time for a racecar is modelled as x= 4 + 5.6t + 2.3t^2
Find the velocity as a function of time.
What is v=5.6 + 4.6t ?
900
A car accelerates from rest at 1.0 m/s2 for 20.0 seconds along a straight road . It then moves at a constant speed for half an hour. It then decelerates uniformly to a stop in 30.0 s. Find the total distance covered by the car.
What is 36,500 meters?
900
This is how far east has a person walked if he travels 350 m in a direction 25° E of N
What is 148m?
900
A ball is launched horizontally from 12m up at an initial speed of 14 m/s. This occurs on the moon, where gravity is 1.62 m/s2. This is how far the ball travels.
What is 53.9m?
900
A race car traveling around a circular path of a radius of 400 m with a speed of 50 m/s. Find the centripetal acceleration of the car.
What is 6.25 m/s2?
1000
|A| = 4
|B| = 3
| hat A * hat B | = 5
Find
( 4 hat A - 3 hat B)*(hat A + 2 hat B)
What is 35?
1000
u=<2,4,5>
v=<−2,6,10>
Find the cross product u x v.
What is <10,−30,20>?
1000
A man walks with his hand on the wall of a building. He follows the building wall until he is exactly 13m from where he started. The building's wall only goes for 8m before taking a 90 degree turn. This is how much longer the wall continues until where the man stopped.
What is 10.25m?
1000
A sailboat is traveling north at 10 km/h, relative to the water. The water is flowing west at 5 km/h, parallel to the shore. This is the velocity of the sailboat relative to ground, and the angle of travel that the sailboat makes with respect to the shore.
Assume that north is positive y and west is negative x. You are looking for the angle from the west to the boat's travel direction.
What is 11.18 km/h, 63.43 degrees?
1000
To approximate the height of a water well, Martha and John drop a heavy rock into the well. 8 seconds after the rock is dropped, they hear a splash caused by the impact of the rock on the water. This is the height of the well. (Speed of sound in air is 340 m/s).
What is 257m?
1000
Find the magnitude and direction from the horizontal of a 40.0 N upward force and 17.0 N horizontal force.
What is 37 degrees at 46.5N?
1000
Bob Gill is attempting to jump as many cars as possible, each 1.7 meters wide and side by side. This is the maximum number of cars Bob Gill can jump with a ramp speed of 40 m/s and an angle above the horizontal of 22° landing at the same height.
What are 65 cars?
1000
An electron moving in a circular track of radius 2 mm at a speed of 2x106 m/s. Find the period of the revolutions
What is 6.3×10−9s?