Try the following:

• get some stuff:
• • a small ball (or some kind of object that will roll - a golfball or marble or toy car is great, but an empty soup can will doin a pinch)
  • get a tape measure (a yardstick or a ruler will also work. Youcan also stretch a piece of string and mark off ruler lengths onthe string to get the total length.)
  • around ten coins
• Measure the distance from a tabletop or kitchen countertop downto the floor. Record the height in meters. (If you measured theheight in inches then convert to meters by dividing the height by39.36)
• Calculate the time it would take any object to fall from theedge of the tabletop to the floor. Use the y-direction displacementformula: y = v_yot + 1/2 a_y t²where
  • y = the height you measured DOWN to the ground
  • v_yo = the initial vertical velocity - should be zerosince an object that rolls off the tabletop will not initially bemoving up or down, but only sideways
  • a_y = the acceleration of gravity DOWN = 9.8m/s²)
  • t = the time

Your Answer:Question 1 options:

Answer

Question 2 (1 point)

Try the following:

• place the small ball on the tabletop, a foot or so from theedge
• get one of the coins
• give the ball a small push so that it rolls off the edge of thetable and place the coin about where the ball lands on thefloor
• Roll the ball off the tabletop again, this time giving a moreforceful push so the ball has more horizontal velocity and againmark its landing spot with a coin
• repeat pushing the ball off the table and marking its landingposition several times, each time with a little more force so as togive the ball a higher horizontal velocity when it leaves thetabletop

What is true of each recorded fall? MARK ALL THAT APPLY!

Question 2 options:

	A) No matter how fast the ball leaves the table horizontally, itstill takes the same amount of time to fall from the tabletop tothe floor
	B) Even when the ball leaves the tabletop with a higher horizontalvelocity it always travels the same distance in the x-direction
	C) When the ball leaves the tabletop with a higher horizontalvelocity it travels farther in the x-direction

Question 3 (1 point)

Try the following:

• gather all the coins off the floor
• On top of the table, make a small ramp out of a thin board or amagazine. Have the bottom edge of the ramp directly on the tableabout a foot from the edge. Use a couple books to support the topof the ramp closer to the middle of the table
• Place a ball at the top of the ramp and allow it to roll downthe ramp, across the foot of tabletop to the edge and go over theedge. Mark where the ball lands with a coin
• Without changing the angle or position of the ramp, repeatedlyrelease the ball from the top of the ramp and mark each landingspot with a coin

What is true of each recorded fall? MARK ALL THAT APPLY!

Question 3 options:

	A) If all factors could be perfectly controlled the ball would hitin the same spot everytime
	B) The landing spots are pretty uniform and the coins are veryclosely grouped on the floor.
	C) Everytime a ball rolls off the table, the table itself gets alittle bit taller

Question 4 (1 point)

• Go tohttps://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion_en.html
• Click the first square that reads \"Intro\"
• You should see a cannon

Just to make sure you're in the right place, what color is thecannon?

Question 4 options:

	A) blue and yellow
	B) red and blue
	C) shades of gray
	D) red and yellow

Question 5 (1 point)

With all the original default settings (height = 10 m, angle = 0degrees, vo = 15 m/s), press the red \"Fire\" button to shoot thecannon. There are three ways to measure the distance the projectiletravels in the x-direction. any of the following will work:

• click and drag the red and white target on the ground over tothe landing spot so that the center of the target is at the end ofthe trajectory
• click and drag the tape measure from the toolbox in the topright of the screen. Place the flat leading edge of the tapemeasure box on the ground directly below the \"+\" of the cannon anddrag the end of the tape to the impact spot
• click and drag the blue time/range/height tool from the toolboxin the top right of the screen. Place the crosshairs over theimpact spot and a small yellow dot should appear. This is probablythe best tool, since you can also read the time the projectilespent in the air and the range and the height above theground.

Which of the following is closest to the actual distance theprojectile travels in the x-direction?

Question 5 options:

	A) 23.8 m
	B) 21.4 m
	C) 19.2 m
	D) 15.0 m

Question 6 (1 point)

• Find the time that it takes a stone to fall 13 m by using they-displacement formula.
• Set the cannon at 13 m and fire horizontally and use the bluetime/range/height gauge to fine the time

How much time does it take to fall 13 m?

Question 6 options:

	A) 15.96 s
	B) 5.8 s
	C) 1.63 s
	D) 0.90 s

Question 7 (1 point)

If a cannon shoots a ball horizontally at 8 m/s, and the ballstarts out 11 m above the floor, how far away from the gun will theball land?

• Solve the formula using the y-displacement formula to find thetime and the x-displacement formula to find the range
• Sent the cannon height at 11m and the initial speed at 8 m/s.Use the blue time/range/height gauge to find the range

What is the horizontal distance the projectile travels?

Question 7 options:

	A) 5.2 m
	B) 12 m
	C) 2.67 m
	D) 15 m

Question 8 (1 point)

Predict the horizontal distance a cannon on a 15 m cliff willshoot if it's horizontal initial velocity is 140 m/s .

Question 8 options:

	A) 207 m
	B) 245 m
	C) 1052 m
	D) 1089 m

Angle Shot

When the cannon is not horizontal, but is aimed either upwardsor downwards, several additional considerations have to bemade.

• we have to find the x and y components of the inital velocity
  • v_ox = v_o cos θ
  • v_oy = v_o sin θ
• we have to get the signs of the y components of velocity andacceleration and displacement correct. If the gun is angled up andgravity pulls down and the displacement is down. You can pick they-coordinate sysytem either positive up/negative down OR positivedown/negative up. It makes no difference which way you pick, butonce you pick everything has to conform to that coordinate system.If we arbitrarily pick positive up
  • the upward initial velocity, v_oy would be up, so itwould be a positive number
  • the gravity, a_y pulls down, so it would be anegative number
  • the rock falls down, so the vertical displacement, y pointsdown, so it would be a negative number
• When we use the y-displacement formula to find time, sincev_oy is no longer zero, as it was in the horizontal shot,we can't cancel the first right hand term. That means we have tosolve the quadratic. Typically using the quadratic formula is thebest choice for doing that. The quadratic formula gives twopossible solutions - choose the one that makes sense (the positiveanswer)

For example: A cannonball leaves a cannon at 15 m/s from 10 mabove ground, fired at an upward 30 degree angle. Find the time tohit the ground and the horizontal range.

Step 1: Y-direction to find Time	Step 2: X-direction to find Range
voy = vo sin θ = 15 sin 30 = 7.5(positive since aimed UP) ay = -9.8 m/s^2 (negative since pulls DOWN) y = -15 m (negative since DOWN) t = the time we're looking for y = voy t + 1/2 ayt2 -15 = 7.5 t + 1/2 (-9.8) t2 0 = -4.9 t2 + 7.5 t+15 Get the coefficients for the quadratic formula a = -4.9 , b = 7.5 , c = 15 t = (-b ± √(b2 - 4 a c)) / (2 a ) t = (-7.5 ± √(7.52 - 4(-4.9)(15))) / (2 (-4.9)) t = -1.14s OR 2.67 s	vox = vo cos θ = 15 cos 30 = 13 ax = 0 (gravity doesn't pull sideways, no airresistance) t = whatever we got from Step 1 = 2.67 s x = the range we're looking for x = vox t + 1/2 axt2 x = (13 m/s)(2.67 s) + 1/2 (0) (2.67)2 x = 34.8 m

Question 9

Set up the cannon so that

• the height is 10 m
• initial speed is 15 m/s
• the angle is 0 degrees, horizontal
• fire the cannon!

Tilt the barrel upwards to 30 degrees and FIRE!

Now, tilt the barrel downwards to 30 degrees and - 3, 2, 1 -FIRE!!!

You should see all three paths that the projectile took. Youmight need the blue measuring device, but MARK ALL THE APPLYTHINGS:

Question 9

	A) When you tilt the gun higher, the shot spends less time in theair
	B) More angle = more time
	C) More time = more range
	D) Since the initial velocity and the height is the same for allthree shots, the time in the air is the same.

Question 10

A cannonball leaves a cannon at 7 m/s from 4 m above ground,fired at an upward 25 degree angle. Find the time to hit theground.

Do this by solving the quadratic and by shooting the virtualcannon

Your Answer:

Question 11

A cannonball leaves a cannon at 15 m/s from 5 m above ground,fired at an upward 30 degree angle. Find the horizontal diistancethe shot travels.

Do this by solving the quadratic and by shooting the virtualcannon to compare.

Your Answer: