5

Icam of engineering students designing catapult t0 Launch small ball at A s0 that it lands in the box . It is known that the initial velocity Vector makes 30" ...

Question

Icam of engineering students designing catapult t0 Launch small ball at A s0 that it lands in the box . It is known that the initial velocity Vector makes 30" angle with the horizontal . determine the maximum launch velocity which the ball will land into the box near the upper right comer of the box (Hint: Be careful about the units of the acceleration pravity-]

Icam of engineering students designing catapult t0 Launch small ball at A s0 that it lands in the box . It is known that the initial velocity Vector makes 30" angle with the horizontal . determine the maximum launch velocity which the ball will land into the box near the upper right comer of the box (Hint: Be careful about the units of the acceleration pravity-]



Answers

A team of engineering students is designing a catapult to launch a small ball at $A$ so that it lands in the box. If it is known that the initial velocity vector makes a $30^{\circ}$ angle with the horizontal, determine the range of launch speeds $v_{0}$ for which the ball will land inside the box.

Yes. Question. We have this situation. So it's a cat about a voice launch. Then he's a building at the maximum height, and then this whole thing takes 1.5 seconds from a to B. And so, um, we want to find out, uh, velocity, the angle of release and height H king. So to do this problem, this is a projectile motion. Okay, so we'll be using Ah, I will be looking at horizontal motion and political emotion separately. Okay, So or the horizontal motion? Either we have no acceleration, so the equation is straightforward. X e a x Times T Yes. This is a Jose data eight times t. So this is, uh, 20 is equal to 1.5 seconds X is equal to 18 ft. So we have to be a because I did, uh, equals two. Oh, Okay. 1.5. Verse 18. So be a cozy data is 18 divided by 1.5. You got 12. Yes. So this is our first equation? Yeah. Then we look at vertical motion. Okay, so, um, uh, displacement the particular this basement during the projectile motion, what they call the spaceman. He from the diagram is H finance 2.5. Right, Because this the whole thing is high. H But during the projectile motion, you don't need to count the initial 2.5 ft. Okay, so, uh, what the girl? This basement is H minus 3.5. And so, um, you can get uh huh. Using B y squared equals two. You know, y squared plus to a top y going to take up where to be positive. Okay, so, uh, you I square the final is zero the the initial SV, a science data, and then this whole thing square minus two G uh, h minus 3.5. So if you re arrange, you get each, uh, finance 2.5 is equal to be a Cy Data. The square sine squared data derived by two G. So H is equal to 3.5 plus yes, square sine squared theta bye bye to G. Okay, if you have an equation for age and then you can also use another equation using, um b y goes to N y. That's a t again going to take upward to be positive. So zero is equal to be a side data by this treaty. Yeah, And then be a site data. If you go to GT, which is 32.2 times 1.5 get 843 Okay, so we have, uh, be a science data equals two for the country. You also have a co science data is equal to house, so engine data is equal to 4.25 You just divide two equations and data is equal to 76.0 degrees. Cool. And then, uh, e eight e a is he Go to Charles. Bye bye. Of course, I data mhm. So, child, divide by course. I 26.0 degrees. You get 49.8. Yes. Uh, second. So this is V a and then got a height. Okay. Height is equal to are 3.5 plus square. Science square data. You got by two g. So this is 2.5 us, okay? Just now we have the A side data to be for the country. For the eight countries where there are two types of 2.2 when you get 39.7 ft. Okay, so that's all for this question.

Well, we have understands along X physical, too. It's not Thanks unless we a times go sign Peter. Multiply by T. Let's plug in numbers So we have a team is equal to read a co sign Preda into 1.5 and listen. Lie state we A is equal to 12 divided by two out, divided by call sign Peter. It was signed Peter, right? And also distance along. Why is equal to asked? No, Tobias not is the initial position less v A times sign. Pita Santina, Dimes de lis one divided by two 80 Square A's ex relation. We know that Lee is equal to D s Divided by D. T right, which is equal to three. A signed Peter be assigned teeter minus 32.2, 22.2 d No ze door is equal to 12. Divided by pull Sign Peter Multiply by scientific data minus 32. Turning to wind Teoh into 1.5. So Peter is equal to stain Universe Keenan. Worse in to 48.3, divided by 12 which is equal to 76.4 our degrees right for their 18 is April to be a call sign pita multiply by t, and this implies they Teoh be a is equal to, um 50.25 feet per second. Right now, h is equal to it is equal to It's not why Les Bee sign Peter do you? Minus one divided by 2 80 square, So each is equal to 3.5 less 50 point Do five. Sign Peter Will Pete, a. Seven dis explained 04 into 1.5 1.5, minus 16 Line six into 1.5 square, which is approximately equal to 39 winds, three feet.

All right. We want the tennis ball from. Why not equals 1.5 m and be not 10.5 m per second and they do not 35 degrees. What is the vertical component of the velocity of tennis fall just before it hits the ground? This is a question related to protect your emotion. Such we use relevant equations first. Let's identify given information. So were given V. Why not equal to be not signed? Data equals 6.2 m per second. VX not equal to be not coast later X not? Why not? And why to solve this problem? Let's first use the equator. The wide equation. Projectile motion. Using Ry. Why not? And B. Why not to solve for T the time? And it's the ground plugging in the relevant variables in solving this equation for tea With the quadratic formula gives two equals 1.45 seconds. So now that we have the time it hits the ground, we can find the vertical component of velocity Y by using the equation of parallel parabolic motion for B. Y. Soviet, Nichols, the Exxon is constant, and B Y equals B y minus Z t is 96.0 to minus 9.81 times 1.45 equals negative 8.2 m per second.

We aim a projectile at a 0.30 point zero m away, where that point has the same height as the initial shooting point. We shoot the projectile with initial horizontal speed of 3.90 m a second. Given this information, we want to determine what the initial vertical speed V. Why not? Is as well as the launch angle fatal? Not in order to answer this question, we need to have a fundamental understanding of the equations of projectile motion First. Let's analyze what's given before we use the equations to solve this problem. So to start off with, we are given the X. Is not equal zero expedition travel to 30.0 m. Why equals why not equal zero? We started under the ground and initial horizontal speed is 3.90 m per second. Using the equation of projectile motion, X equals X. B. X 90. With economical zero. We have T. M. T. Equals X. Or V. X. Or time of flight 7.69 seconds. next. If we use the equation for y motion where we were wine and why not Are zero? We can solve the V. Why not? In terms of tea as well, why not equal to have g. T. Or 37.7 m per second? Then we can use that the direction of the arc tangent, inverse tangent over the initial vertical speed over the initial horizontal speed. Be why not over the extent to obtain initial angle 84.9 degrees?


Similar Solved Questions

5 answers
Whkch 0l the following carbonations is most stablo?
Whkch 0l the following carbonations is most stablo?...
5 answers
'2 01 0 WOJJ quoudos JuI ~ens 3q80- ajaq* 'Sp (5) { % = (2) 6 1Og S2p1OS UTInE[DBTN J41 pULI '(2) [ JOg SOHJOS ULInepBJA 341 pu! '0 = 2 48 ?AA[BUB SI Kqm uejdxd I = (0) f Ia8 pUe Fus (=) f 12T
'2 01 0 WOJJ quoudos JuI ~ens 3q80- ajaq* 'Sp (5) { % = (2) 6 1Og S2p1OS UTInE[DBTN J41 pULI '(2) [ JOg SOHJOS ULInepBJA 341 pu! '0 = 2 48 ?AA[BUB SI Kqm uejdxd I = (0) f Ia8 pUe Fus (=) f 12T...
5 answers
Picben 0]POeteet Eue [a) Perdd]USn0etans
Picben 0] POeteet Eue [a) Perdd] USn 0etans...
5 answers
Prove that AnB = TuB by giving containment proof. (That is, prove that the lelt side is a subset o the right side and that the right side is a subset of the lelt side)_ (b) Venn diagram proof.
Prove that AnB = TuB by giving containment proof. (That is, prove that the lelt side is a subset o the right side and that the right side is a subset of the lelt side)_ (b) Venn diagram proof....
5 answers
Evaluate the indefinite integral:sec? (8x) tan? (8x) dx
Evaluate the indefinite integral: sec? (8x) tan? (8x) dx...
5 answers
Which of the following the derivative & for the plane curve defined by the equations x(t) = / _ 4,Mt) = 2r _ 6,am4 "2 < $37Select the correct answer below:
Which of the following the derivative & for the plane curve defined by the equations x(t) = / _ 4,Mt) = 2r _ 6,am4 "2 < $37 Select the correct answer below:...
5 answers
(1 point) Find the absolute maximum and absolute minimum values of x2 1 f(x) = on the interval x2 + 1 [-5,5].1. Find the absolute maximum of f on the interval_ Answer:2. Find the absolute minimum of f on the interval: Answer:
(1 point) Find the absolute maximum and absolute minimum values of x2 1 f(x) = on the interval x2 + 1 [-5,5]. 1. Find the absolute maximum of f on the interval_ Answer: 2. Find the absolute minimum of f on the interval: Answer:...
5 answers
A-[:3!" Fir nll rer #? thal GaisoTivi -IT 70r -na1 TTu; Ccinenm ~a |Tulicr#LLTanatolemtr IAoTrnrin matix &i * .17 tbc -ixctanlaRt ute WCTl?Gin" chat TctizeCL Tir u: lirtur trntisLnwa itu tha ecICs: Il Iine DrwieI: ev orth KCEAL;' Mfua | Mc'
A-[:3!" Fir nll rer #? thal GaisoTivi -IT 70r -na1 TTu; Cc inenm ~a |Tulicr #LL Tanato lemtr IAoTrnrin matix &i * . 17 tbc -ix ctanla Rt ute WCTl?Gin" chat TctizeCL Tir u: lirtur trntisLnwa itu tha ecICs: Il Iine DrwieI: ev orth KCEAL;' Mfua | Mc'...
5 answers
7z - 3 In the Laurent series expansion of f(z) = valid for 0<lz _ 1/ <1, z(z _ 1) we find a _230 2
7z - 3 In the Laurent series expansion of f(z) = valid for 0<lz _ 1/ <1, z(z _ 1) we find a _2 3 0 2...
5 answers
Find the interest on the following loan.85394 at 2%; loan made on August 17 and due December 14The simple interest for this loan is $ (Round to the nearest cent as needed:)
Find the interest on the following loan. 85394 at 2%; loan made on August 17 and due December 14 The simple interest for this loan is $ (Round to the nearest cent as needed:)...
5 answers
12. [-/3 Points]DETAILSZILLDIFFEQMODAP1I 4.3.035.MI:Solve the given initial-value problem.Y'14y" + 49y' 0, y(o) =0, Y(0) = 1, Y'(0) = -12y(x)
12. [-/3 Points] DETAILS ZILLDIFFEQMODAP1I 4.3.035.MI: Solve the given initial-value problem. Y' 14y" + 49y' 0, y(o) =0, Y(0) = 1, Y'(0) = -12 y(x)...
5 answers
Whizh oellna vilid resonance structure of the following molecule?C1?CH;HCCHA
Whizh oellna vilid resonance structure of the following molecule? C1? CH; HC CHA...
4 answers
Find the maximum and minimum values of thefunction f(x,y,z,t)=x+y+z+tf(x,y,z,t)=x+y+z+t subject tothe constraint x2+y2+z2+t2=256x2+y2+z2+t2=256. Maximum valueis , occuring at points (positive integer or"infinitely many"). Minimum value is , occuringat points (positive integer or "infinitely many").
Find the maximum and minimum values of the function f(x,y,z,t)=x+y+z+tf(x,y,z,t)=x+y+z+t subject to the constraint x2+y2+z2+t2=256x2+y2+z2+t2=256. Maximum value is , occuring at points (positive integer or "infinitely many"). Minimum value is , occuring at points (positive integer or &...
5 answers
An experiment showed that as the amount of alcohol consumeddecreases, weight decreases. This is an example of a:
An experiment showed that as the amount of alcohol consumed decreases, weight decreases. This is an example of a:...
5 answers
2 all values 8 for which the power seriesn3"convergent:
2 all values 8 for which the power series n3" convergent:...
5 answers
10. [-/2 Points]DETAILSSCALCETBM 11.8.017.Find the radius of convergence R, of the series _x+9) 9" In(n)Find the interval, I, of convergence of the series_ (Enter your answer using interva notationNeed Help?Read kt
10. [-/2 Points] DETAILS SCALCETBM 11.8.017. Find the radius of convergence R, of the series _ x+9) 9" In(n) Find the interval, I, of convergence of the series_ (Enter your answer using interva notation Need Help? Read kt...
5 answers
Find gcneral solution to the ODE: 3"(0) + ~"(0) sc(:" 0 _
Find gcneral solution to the ODE: 3"(0) + ~"(0) sc(:" 0 _...

-- 0.021227--