Question

2. A baseball thrown from the outfield, a golf ball, or a thrown football, all will follow a trajectory (path) that has horizontal as well as vertical displacement components. If we neglect the air friction on the ball, the path will be a perfect parabolic trajectory. The equations for the displacement of the ball are: Take gravity g as 9.81 meters per second, and the initial velocity, Vo, equal to 35 meters/second. Use Excel to show the ball trajectory for different launch angles, for that: Plot y(t) vs. x(t) for various launch angles (20, 30, 45, 60, and 70 degrees). Your a) final plot should look similar to the figure below Range R vs Launch Angle e for a Given Initial Velocity V Launch Angle of Elevation e Parabolic Trajectories 2 Range Determine the range and maximum height for each trayectory b)

Answer 1

Ball trajectory

given		intial velocity(Vo)	35	m/sec
		g	9.81	m/sec^2
		intial displcement	Xo	0	m
			Yo	0	m
		displacement equation	X(t)	Xo+(Vox)t	m
			Y(t)	Yo+(Voy)t-(1/2)gt^2	m

launching angle (ɵ)	20	30	45	60	70
Vox(m/sec)	32.88924	30.31088913	24.74874	17.5	11.97071
Voy(m/esc)	11.97071	17.5	24.74874	30.3108891	32.88924

	intial angle (ɵ)	20
time(t)	X(t)	Y(t)
0	0	0
0.244051	8.026654657	2.629317
0.488102	16.05330931	4.674341
0.732153	24.07996397	6.135073
0.976204	32.10661863	7.011512
1.220255	40.13327329	7.303658
1.464306	48.15992794	7.011512
1.708357	56.1865826	6.135073
1.952409	64.21323726	4.674341
2.19646	72.23989191	2.629317
2.440511	80.26654657	0

	intial angle (ɵ)	30
time(t)	X(t)	Y(t)
0	0	0
0.3567788	10.81428257	5.619266
0.7135576	21.62856513	9.989806
1.0703364	32.4428477	13.11162
1.4271152	43.25713026	14.98471
1.783894	54.07141283	15.60907
2.1406728	64.88569539	14.98471
2.4974516	75.69997796	13.11162
2.8542304	86.51426052	9.989806
3.2110092	97.32854309	5.619266
3.567788	108.1428257	0

	intial angle (ɵ)	45
time(t)	X(t)	Y(t)
0	0	0
0.504561	12.4872579	11.23853
1.009123	24.9745158	19.97961
1.513684	37.4617737	26.22324
2.018246	49.9490316	29.96942
2.522807	62.4362895	31.21814
3.027368	74.9235474	29.96942
3.53193	87.4108053	26.22324
4.036491	99.8980632	19.97961
4.541053	112.3853211	11.23853
5.045614	124.872579	0

	intial angle (ɵ)	60
time(t)	X(t)	Y(t)
0	0	0
0.617959	10.81428257	16.8578
1.235918	21.62856513	29.96942
1.853877	32.4428477	39.33486
2.471836	43.25713026	44.95413
3.089795	54.07141283	46.82722
3.707754	64.88569539	44.95413
4.325713	75.69997796	39.33486
4.943672	86.51426052	29.96942
5.561631	97.32854309	16.8578
6.17959	108.1428257	0

	intial angle (ɵ)	70
time(t)	X(t)	Y(t)
0	0	0
0.670525	8.026654657	19.84775
1.34105	16.05330931	35.28488
2.011574	24.07996397	46.31141
2.682099	32.10661863	52.92733
3.352624	40.13327329	55.13263
4.023149	48.15992794	52.92733
4.693674	56.1865826	46.31141
5.364198	64.21323726	35.28488
6.034723	72.23989191	19.84775
6.705248	80.26654657	0

Parabolic Trajectories 60 50 40 intialangle (e)-20 3 30 intialangle (e)-30 intialangle(e)-45 20 intialangle (e)-60 intialangle (e)-70 10 20 80 100 120 40 140 Range

(B) the ranges and maximum height:-

intial angle (ɵ)	20	30	45	60	70
X-range(m)	0 to 80.26654657	o to 108.1428257	o to 124.872579	o to 108.1428257	0 to 80.26654657
Y-range(m)	0 to7.303658	0 to 15.60907238	0 to 31.21814475	o to 46.8272713	0 to 55.13263
maximum height(m)	7.30365844	15.60907238	31.21814475	46.82721713	55.13263106