Page 1 – Cliff Problem
Jan 01, 2016
V = 9.21 m/s t = 2.17 s
Fill in your H/V table of XViVfat1. How far out does she land?2. How high is the cliff?3. What is the velocity of impact in VC
Notation?4. What is the speed of impact?5. What is the velocity of impact? (in AM
Notation)
V = 9.21 m/s t = 2.17 sFill in your H/V table of XViVfat1. How far out does she land?2. How high is the cliff?3. What is the velocity of impact in VC Notation?4. What is the speed of impact?5. What is the velocity of impact? (in AM Notation)
H VX ? ?Vi 9.21 m/s 0 (cliff)Vf 9.21 m/sa 0 -9.8 m/s/st 2.17 s 2.17 s
Horiz:X = (9.21)(2.17) = 19.9857 m ≈ 20. m
Vert:Vf = Vi + at = 0 + (-9.8)(2.17) = -21.266 m/s ≈ 21.3 m/sX = Vi t + 1/2at2 = 0 + 1/3(-9.8)(2.17)2 = -23.07361 m
So she lands about 20. m out, the cliff is 23 m tall, and her velocity of impact in VC notation is:9.21 m/s x + -21.3 m/s y, the speed is the hypotenuse of that √(9.212+21.2662) = 23.1747 m/s so
her speed is about 23.2 m/s
In angle magnitude notation her velocity looks like:
The magnitude is the speed we calculated, and the angleindicated is θ = tan-1(21.266/9.21) = 66.6o
9.21
21.266
V = 29.9 m/s
Find vector componentsFill in your H/V table of X Vi Vf a t1. Find the hang time2. Find the range3. Find Speed at highest point.4. Greatest Height the ball reaches
angle = 25.0o
V = 29.9 m/s
Find vector componentsFill in your H/V table of X Vi Vf a t1. Find the hang time2. Find the range3. Find Speed at highest point.4. Greatest Height the ball reaches
First, resolve the vector into components:Vx = (29.9 m/s)cos(25o) = 27.10 m/s, Vy = (29.9 m/s)sin(25o) = 12.64 m/s – these are your initial velocities. Now
we aet up the H/V table
H VX ? 0 (level ground)Vi 27.10 m/s 12.64 m/sVf 27.10 m/s -12.64 m/s (level ground)a 0 -9.8 m/s/st ? ?
Vert:Find t using Vi = Vf + at, -12.64 = 12.64 + (-9.8)t, t = 2.579 s, which is the hang time
Horiz:Find X using X = Vi t = (27.10)(2.579 s) = 69.9 m which is the range
At the highest point Vert:Vf = 0 (top)So the speed is purely horizontal = 27.1 m/s in this case, and the greatest height is Vf2 = Vi2 + 2aX, 02 = (12.64)2 + 2(-9.8)X, X = 8.147 m ≈ 8.15 m
angle = 25.0o
Vectors - Finding Components - step by step
TOC
Step 1: Find the Trig angle – ACW from x axis
0o Or 360o
90o
180o
270o
27o
51o
15o
17o
This is the trig angle
T = 270 – 15 = 255o T = 270 + 51 = 321o
T = 360 – 17 = 343o
OR
T = -17o
Vectors - Try this yourself
TOC
Get out your calculatortype:sin 90 <ENTER>1????If not <2nd?> MODECursor arrows to “Degree”<ENTER> <CLEAR>Try again (sin 90)
Vectors - Finding Components - step by step
TOC
Step 2: Figure the sidesusing Cos and Sin:x = mag Cos()y = mag Sin()(iff = trig angle)
x = (12 m)Cos(153o) = -10.692 m
= 180o – 27o = 153o
y = (12 m)Sin(153o) = +5.448 m
12 m
27o
Vectors - Finding Components - step by step
TOC
Step 3: Write it in Vector Component notation:
Vector = -11 m x + 5.4 m y (With sig figs)Reality Check:
(+ and -), relative size
12 m
27o
Vectors - Try this yourself
TOC
23.0 m/s31.0o
1. Draw the Components2. Figure the components with sin and cos3. Write the answer in VC Notation
-11.8 m/s x + 19.7 m/s y
= 90 + 31 = 121o
23cos(121) x + 23sin(121) y-11.846 x + 19.715 y
22.8 km x + 14.4 km y W
32.2o
27.0 km
= 32.2o
27.0cos(32.2) x + 27.0sin(32.2) y22.84721549 14.3876594522.8 km x + 14.4 km y
37 m x + -19 m y W
42 m
27o
= 360 – 27 = 333o
42cos(333) x + 42sin(333) y37.42227402 -19.0676009937 m x + -19 m y
-4.9 ft x + 1.1 ft y W
5.0 feet77o
= 90 + 77 = 167o
5cos(167) x + 5sin(167) y-4.871850324 1.124755272-4.9 ft x + 1.1 ft y
68 N x + -87 N y W
110.0 N38o
= 270 + 38 = 308o
110.0cos(308) x + 110.0sin(308) y67.72276229 -86.681182968 N x + -87 N y
-4.3 m/s x + -2.5 m/s y W
5.0 m/s
30.0o
= 180 + 30.0 = 210.0o
5.0cos(210.0) x + 5.0sin(210) y-4.330127019 -2.5-4.3 m/s x + -2.5 m/s y
Vectors - VC + VC - step by step
TOC
Given these Vectors:
A: 2.3 m x + 3.4 m yB: 7.4 m x + 1.2 m yA+B = 9.7 m x + 4.6 m y
Any Questions??????(This is why VC vectors are our friends)
Vectors - VC to AM - step by step
TOC
Given this VC Vector: 5.1 m x + -1.7 m y
2. Find the angle:
1. Draw the vector:5.1 m x
-1.7 m y
Tan = opp/adj
adj
opp
= tan-1(1.7/5.1) = 18.435o = 18o (s.f.)
3. Find the Magnitude:opp2 + adj2 = hyp2 hyp = (5.12 + 1.72) = 5.376 = 5.4 m
3.9 m, 30.o W
Draw this vector, and find its magnitude and the angle it forms with the x-axis: (label your angle) 3.4 m x + 2.0 m y
3.4 m
2.0 m3.9 m
30.o
27 m/s, 56o W
Draw this vector, and find its magnitude and the angle it forms with the y-axis: (label your angle) -22 m/s x + 15 m/s y
-22 m/s
15 m/s
27 m/s56o
17.5 N, 31.0o W
Draw this vector, and find its magnitude and the angle it forms with the y-axis: (label your angle) 9.00 N x + -15.0 N y
9.00 N
-15.0 N17.5 N
31o
8.19 , 59.8o W
Add these two angle magnitude vectors, and express their sum as an angle magnitude vector, finding the angle it forms with the x-axis
48.0o
7.00
A B
9.00
78.0o
1. AM to VC AM to VC2. VC + VC3. AM to VC
A = 4.684 x + 5.202 yB = -8.803 x + 1.871 yA + B = -4.119 x 7.073 y
Mag = √(4.1192+7.0732) = 8.19
θ = Tan-1(7.073/4.119) = 59.8o
Current: 1.2 m/sFind:
•Time to cross•Where it lands•Speed as seen from above•Angle to go straight across?
120 m
Boat 3.5 m/s
Current: 1.2 m/s
Find:•Time to cross•Where it lands•Speed as seen from above•Angle to go straight across?
AC DSX 120 m ?V 3.5 m/s 1.2 m/st ? ?
AC: Find time using V = X/t, 3.5 = 120/t, t = 34.29 s which is true on the DS side too
DS:Find X using V = X/t, 1.2 = X/34.29 s, X = 41.14 m
Speed is the hypotenuse of the velocity vector:= √(3.52+1.22) = 3.7 m/s
120 m
Boat 3.5 m/s
3.5 m/s1.2 m/s
θ = Sin-1(1.2/3.5) = 20. o