Question

ENES 100 Due 11/14/2018 Homework #6 Submit all your work in a thumb drive or via email using the appropriate filenames 1. When an object is launched from the ground with an initial velocity of vo at an angle of 0o, the horizontal and vertical displacements of the object travel before it hits ground can be written as functions of time t: x(t) - vo t cos(e) Uo Figure 1: Projectile of an object. A baseball has been tossed with the initial velocity 20 m/s with the angle 30° from the ground. Use g 9.81 m/s2. Construct a spreadsheet to calculate the horizontal and vertical displacements of the ball for time t ranging from 0 to 2.1 seconds in increments of 0.02 seconds. Name your worksheet as "Analysis". Plot the functions x(t) and y(t) verse time t (i.e. x-t and y-t graphs) on the same graph. Plot the trajectory of the baseball (i.e. y v.s. x graph) Using the graph and your data to determine the maximum height reached by the ball and the horizontal distances it travels before it strikes the ground. Insert comments on the cells that have maximum height and the longest distance it travels Save your spreadsheet as yourname partA.xlsx with results with comment from d) and charts from b) and c) If the initial velocity changes to 30 m/s and the tossing angle changes from 30o to 45o what will be the maximum height reached by the ball? When will the ball hit the ground? Use time increment 0.04 sec. Adjust your numbers in the analysis worksheet accordingly (maybe you need to add more time in your time t too, since it will takıe longer time for the ball to reach the ground). Save your worksheet as yourname partB.xlsx. a. b. c. d. e. f.

Answer 1

Initial conditions:

Initial conditions: x(t) = 20 * t * cos 30 = 17.32t y(t) = 20 * t * sin 30 - 0.5 * 9.81^2 = 10t - 4.905t^2 Code for the A3 cell: Putin A2 and copy throughout the column, delete after 2.1 A2 + 0.02 Code for B2: Copy same as before 17.32 * B2 Code for C2: Copy same as before = (10 * A2) - (4.905 * (A2)^2) \r\n x(t)vs t: \r\n y(t) vs t graph: \r\n y(t) vs x(t) graph: \r\n Maximum height: 5.096838m Horizontal range: 36.372. Set of conditions: x(t) = 30 * t * cos 45 = 21.21t y(t) = 30 * t * sin 45 -0.5 * 9.81t^2 = 21.21t - 4.905t^2 Chart building is same as before: x vs t: \r\n y vs t: \r\n x vs y \t\n Maximum height: 22.92883m Maximum range: 92.6272m Time of flight: 4.32s

$y(t) = 20*t*\sin30 -0.5*9.81t^2= 10t - 4.905t^2$

Code for the A3 cell : Put 0 in A2 and copy throughout the column, delete after 2.1

A2+0.02

Code for B2: Copy same as before

17.32*B2

Code for C2: Copy same as before

=(10*A2)-(4.905*(A2)^2)

_________________________________________________

Data

Time	X position	Y Position
0	0	0
0.02	0.3464	0.198038
0.04	0.6928	0.392152
0.06	1.0392	0.582342
0.08	1.3856	0.768608
0.1	1.732	0.95095
0.12	2.0784	1.129368
0.14	2.4248	1.303862
0.16	2.7712	1.474432
0.18	3.1176	1.641078
0.2	3.464	1.8038
0.22	3.8104	1.962598
0.24	4.1568	2.117472
0.26	4.5032	2.268422
0.28	4.8496	2.415448
0.3	5.196	2.55855
0.32	5.5424	2.697728
0.34	5.8888	2.832982
0.36	6.2352	2.964312
0.38	6.5816	3.091718
0.4	6.928	3.2152
0.42	7.2744	3.334758
0.44	7.6208	3.450392
0.46	7.9672	3.562102
0.48	8.3136	3.669888
0.5	8.66	3.77375
0.52	9.0064	3.873688
0.54	9.3528	3.969702
0.56	9.6992	4.061792
0.58	10.0456	4.149958
0.6	10.392	4.2342
0.62	10.7384	4.314518
0.64	11.0848	4.390912
0.66	11.4312	4.463382
0.68	11.7776	4.531928
0.7	12.124	4.59655
0.72	12.4704	4.657248
0.74	12.8168	4.714022
0.76	13.1632	4.766872
0.78	13.5096	4.815798
0.8	13.856	4.8608
0.82	14.2024	4.901878
0.84	14.5488	4.939032
0.86	14.8952	4.972262
0.88	15.2416	5.001568
0.9	15.588	5.02695
0.92	15.9344	5.048408
0.94	16.2808	5.065942
0.96	16.6272	5.079552
0.98	16.9736	5.089238
1	17.32	5.095
1.02	17.6664	5.096838
1.04	18.0128	5.094752
1.06	18.3592	5.088742
1.08	18.7056	5.078808
1.1	19.052	5.06495
1.12	19.3984	5.047168
1.14	19.7448	5.025462
1.16	20.0912	4.999832
1.18	20.4376	4.970278
1.2	20.784	4.9368
1.22	21.1304	4.899398
1.24	21.4768	4.858072
1.26	21.8232	4.812822
1.28	22.1696	4.763648
1.3	22.516	4.71055
1.32	22.8624	4.653528
1.34	23.2088	4.592582
1.36	23.5552	4.527712
1.38	23.9016	4.458918
1.4	24.248	4.3862
1.42	24.5944	4.309558
1.44	24.9408	4.228992
1.46	25.2872	4.144502
1.48	25.6336	4.056088
1.5	25.98	3.96375
1.52	26.3264	3.867488
1.54	26.6728	3.767302
1.56	27.0192	3.663192
1.58	27.3656	3.555158
1.6	27.712	3.4432
1.62	28.0584	3.327318
1.64	28.4048	3.207512
1.66	28.7512	3.083782
1.68	29.0976	2.956128
1.7	29.444	2.82455
1.72	29.7904	2.689048
1.74	30.1368	2.549622
1.76	30.4832	2.406272
1.78	30.8296	2.258998
1.8	31.176	2.1078
1.82	31.5224	1.952678
1.84	31.8688	1.793632
1.86	32.2152	1.630662
1.88	32.5616	1.463768
1.9	32.908	1.29295
1.92	33.2544	1.118208
1.94	33.6008	0.939542
1.96	33.9472	0.756952
1.98	34.2936	0.570438
2	34.64	0.38
2.02	34.9864	0.185638
2.04	35.3328	-0.01265
2.06	35.6792	-0.21486
2.08	36.0256	-0.42099
2.1	36.372	-0.63105

Graph:

x(t)vs t:

y(t) vs t graph:

y(t) vs x(t) graph:

Maximum height: 5.096838m
Horizontal range : 36.372.

___________________________________________________________________

Set of conditions:

$x(t) = 30*t*\cos45 = 21.21t$

$y(t) = 30*t*\sin45-0.5*9.81t^2= 21.21t - 4.905t^2$

Chart building is same as before:

DATA:

Time	X position	Y Position
0	0	0
0.04	0.8484	0.840552
0.08	1.6968	1.665408
0.12	2.5452	2.474568
0.16	3.3936	3.268032
0.2	4.242	4.0458
0.24	5.0904	4.807872
0.28	5.9388	5.554248
0.32	6.7872	6.284928
0.36	7.6356	6.999912
0.4	8.484	7.6992
0.44	9.3324	8.382792
0.48	10.1808	9.050688
0.52	11.0292	9.702888
0.56	11.8776	10.33939
0.6	12.726	10.9602
0.64	13.5744	11.56531
0.68	14.4228	12.15473
0.72	15.2712	12.72845
0.76	16.1196	13.28647
0.8	16.968	13.8288
0.84	17.8164	14.35543
0.88	18.6648	14.86637
0.92	19.5132	15.36161
0.96	20.3616	15.84115
1	21.21	16.305
1.04	22.0584	16.75315
1.08	22.9068	17.18561
1.12	23.7552	17.60237
1.16	24.6036	18.00343
1.2	25.452	18.3888
1.24	26.3004	18.75847
1.28	27.1488	19.11245
1.32	27.9972	19.45073
1.36	28.8456	19.77331
1.4	29.694	20.0802
1.44	30.5424	20.37139
1.48	31.3908	20.64689
1.52	32.2392	20.90669
1.56	33.0876	21.15079
1.6	33.936	21.3792
1.64	34.7844	21.59191
1.68	35.6328	21.78893
1.72	36.4812	21.97025
1.76	37.3296	22.13587
1.8	38.178	22.2858
1.84	39.0264	22.42003
1.88	39.8748	22.53857
1.92	40.7232	22.64141
1.96	41.5716	22.72855
2	42.42	22.8
2.04	43.2684	22.85575
2.08	44.1168	22.89581
2.12	44.9652	22.92017
2.16	45.8136	22.92883
2.2	46.662	22.9218
2.24	47.5104	22.89907
2.28	48.3588	22.86065
2.32	49.2072	22.80653
2.36	50.0556	22.73671
2.4	50.904	22.6512
2.44	51.7524	22.54999
2.48	52.6008	22.43309
2.52	53.4492	22.30049
2.56	54.2976	22.15219
2.6	55.146	21.9882
2.64	55.9944	21.80851
2.68	56.8428	21.61313
2.72	57.6912	21.40205
2.76	58.5396	21.17527
2.8	59.388	20.9328
2.84	60.2364	20.67463
2.88	61.0848	20.40077
2.92	61.9332	20.11121
2.96	62.7816	19.80595
3	63.63	19.485
3.04	64.4784	19.14835
3.08	65.3268	18.79601
3.12	66.1752	18.42797
3.16	67.0236	18.04423
3.2	67.872	17.6448
3.24	68.7204	17.22967
3.28	69.5688	16.79885
3.32	70.4172	16.35233
3.36	71.2656	15.89011
3.4	72.114	15.4122
3.44	72.9624	14.91859
3.48	73.8108	14.40929
3.52	74.6592	13.88429
3.56	75.5076	13.34359
3.6	76.356	12.7872
3.64	77.2044	12.21511
3.68	78.0528	11.62733
3.72	78.9012	11.02385
3.76	79.7496	10.40467
3.8	80.598	9.7698
3.84	81.4464	9.119232
3.88	82.2948	8.452968
3.92	83.1432	7.771008
3.96	83.9916	7.073352
4	84.84	6.36
4.04	85.6884	5.630952
4.08	86.5368	4.886208
4.12	87.3852	4.125768
4.16	88.2336	3.349632
4.2	89.082	2.5578
4.24	89.9304	1.750272
4.28	90.7788	0.927048
4.32	91.6272	0.088128

x vs t:

y vs t:

x vs y:

Maximum height : 22.92883m

Maximum range: 91.6272m

Time of flight : 4.32s