Kinematics
Vectors
Trig
Projectiles
100
A soccer ball originally at rest is kicked, rolling 15 m in 3 s. What was its speed?
s=d/t={15m}/{3s}=5m/s
100
What shape represents a vector?
An arrow
100
What is the difference between regular trig functions and inverse trig functions?
Regular trig functions find side lengths, inverse trig functions find angles.
100
What is the x and y acceleration of an object in projectile motion?
a_x=0
a_y=g=-9.81m/s^2
200
A cliff diver jumps off an 18 meter cliff. How long does it take them to land in the water?
\Delta x=v_it+1/2at^2
-18m=(0m/s)t+1/2(-9.81m/s^2)t^2
t=\sqrt{{-18m}/{1/2(-9.81m/s^2)}}=3.7s
200
How do you align vectors in order to add them?
Line them up tip to tail
200
What equation do you use to find the adjacent side of a right triangle given the angle and the opposite side?
a=o/tan(\theta)
200
A cannonball is launched with an initial velocity of 12 m/s at a 35 degree angle. What are the x and y components of the initial velocity?
v_{ix}=12xxcos(35^@)=9.83m/s
v_{iy}=12xxsin(35^@)=6.88m/s
300
What is the initial velocity of an object that travels 124 meters in 3.7 seconds with an acceleration of 4.3 m/s^2 ?
\Delta x=v_it+1/2at^2
124m=v_i(3.7s)+1/2(4.3m/s^2)(3.7s)^2
v_i={124m-1/2(4.3m/s^2)(3.7s)^2}/{3.7s}=25.6m/s
300
Draw the resultant displacement vector:
2 meters East plus 3 meters South
300
What is the x-component of a 20 m/s initial velocity vector pointing at an angle of 146 degrees from the positive x-axis?
x=h*cos(theta)=20m/sxxcos(146^@)=-16.6m/s
300
A cannonball is launched with an initial velocity of 12 m/s at a 35 degree angle. If you knew the time, what equation would you use to find the horizontal displacement?
\Delta x=v_{ix}t
400
What is the acceleration of a car that went from 7 m/s to 21 m/s over a span of 83 meters?
v_f^2=v_i^2+2a\Delta x
(21m/s)^2=(7m/s)^2+2a(83m)
a= {(21m/s)^2-(7m/s)^2}/{2(83m)}=2.36m/s^2
400
A jogger begins running South at 5 m/s. She turns and runs 3 m/s West. What is the magnitude of her total velocity?
\vec{v}=\sqrt{(-5m/s)^2+(-3m/s)^2}=\sqrt{34}m/s=5.83m/s
400
A jogger begins running 3 m/s at 14 degrees north of east. She then runs 4.5 m/s at 37 degrees west of north.What is the magnitude and direction of her total velocity?
x_1=3xxcos(14)=2.91m/s
y_1=3xxsin(14)=0.73m/s
x_2=4.5xxcos(127)=-2.71m/s
y_2=4.5xxsin(127)=3.59m/s
v_x=x_1+x_2=2.91m/s-2.71m/s=0.20m/s
v_y=y_1+y_2=0.73m/s+3.59m/s=4.32m/s
\theta=tan^-1(4.32/0.20)=87.35^@
400
What is the relation between projectile motion and all of the vector questions we've been doing?
Projectile motion includes x and y components, meaning we have to use vector addition properties in order to solve for final values.