Dots & Crosses
Find the dot product of the following:
|a| = 4
|b| = 6
Angle between is 60 degrees.
What is 12?
You get this when you integrate 5 from 7 to 11.
What is 20?
You throw a ball 50m. Your dog runs to it and brings it straight back to you. This is the ball's displacement.
What is zero?
The speed limit on a road is 55 miles per hour. Gregory is taking a physics course, and he thinks that if he drives backwards, he can go as fast as he wants because his velocity (from his perspective if he is facing in the positive direction) will be negative and therefore less than 55 miles per hour. Is Gregory right about his velocity?
No need for Jeopardy format answers.
Gregory is right about his velocity being negative from his perspective, and therefore less than 55 miles per hour.
You throw the ball 50m for your dog. Your dog's position as it chases the ball is modelled by the function:
x = 1 + 2t2
This is your dog's acceleration.
What is 2?
Find the cross product of the following:
|a| = 4
|b| = 10
Angle between is 30 degrees.
What is 20?
You get this when you integrate 0.5x from 0 to 3.
Looking for a fraction.
What is nine fourths (9/4)?
You throw a ball 50m. Your dog runs to it and brings it straight back to you. This is the ball's distance travelled.
What is 100m?
The speed limit on a road is 55 miles per hour. Gregory is taking a physics course, and he thinks that if he drives backwards, he can go as fast as he wants because his velocity (from his perspective if he is facing in the positive direction) will be negative and therefore less than 55 miles per hour. Based on Physics concepts, will Gregory avoid a speeding ticket?
No need for Jeopardy format answers.
No. Speed is the magnitude of velocity. If Gregory has a velocity of -60 miles per hour, he is still speeding.
A sports car goes from 0 m/s to 60 m/s in 3.5 seconds.
This is its average acceleration.
Round to 3 SF.
What is 17.1 m/s2?
Find the dot product of the following:
a = 12i -3j +14k
b = 6i -15k
What is -138?
You get this when you integrate x2+3 from 0 to 5.
What is 56.666 or 170/3?
(both are acceptable)
The ball you threw for your dog only travelled 20m away from you before getting stuck in a tree branch 5m off the ground. This is the ball's position vector.
Assume that you are standing at 0,0. The positive y axis is up, the positive x axis is away from you.
What is <20, 5> ?
A sports car's position is modelled by the equation x = 4(m/s)t + 5(m/s2)t2.
This is the equation that models the sports car's velocity.
What is v = 4(m/s) + 10(m/s2)t?
A racecar's position is modelled by the function
x = 9 - 4t + 6t2
where position is in meters and time is in seconds.
This is the racecar's acceleration at 5 seconds.
What is 12 m/s2?
Find the cross product of the following:
a = < 1, 3, 1 >
b = <2, 0, 1 >
What is < 3, 1, -6 >?
You get this when you integrate the following from 0 to 2:
4.0 + 8.0t - 4.9t2
Round to 2 significant figures.
What is 11?
You throw the ball 50m away for your dog. It gets to the ball, then carries it 12m more away from you, then climbs a staircase that takes it 10m horizontal to you and 5m vertical.
This is the ball's distance travelled.
Round to 3 SF.
What is 73.2m?
A sports car's acceleration is modelled by the equation a = 8 m/s2.
The sports car starts at rest.
This is the equation that models the sports car's velocity.
What is v = 8(m/s2)t?
A car moving at 80 mph has a speed of 35.8 m/s. This is the acceleration it would have if it took 5.0 s to come to a complete stop.
What is -7.16 m/s2?
Vector A has a magnitude of 8 and lies along the positive y axis.
Vector B has a magnitude of 9 and lies along the negative y axis.
Find the dot product.
What is 72?
Note: Cosine of 180 is what?
You get this when you integrate the following from 0 to 1:
6.0 - 5.0t + 12t2 - 0.25t3
Round to 2 SF.
What is 7.4?
You throw the ball 50m away for your dog. It gets to the ball, then carries it 12m more away from you, then climbs a staircase that takes it 10m horizontal to you and 5m vertical.
This is the ball's displacement.
Use vector notation. The positive y axis is straight up, the positive x axis is away from you, the positive z axis is in the direction the dog walked horizontal to you.
What is <62, 5, 10>?
A racecar is rounding a tight turn. Its velocity (in m/s) is modelled by the following equation:
v = <56-5t, 6t>
This is its speed after 5 seconds.
Round to 2 SF.
What is 43 m/s?
A baseball is pitched at 40 m/s in a Major League game. The batter hits the ball on a line drive straight toward the pitcher at 50 m/s. This is the acceleration of the ball if it was in contact with the bat for 0.03 s.
Assume the positive direction is towards the batter.
What is -3000 m/s2?