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(Circle one) Question 1: 50% Projectile is launched at 25° above horizontal at 55mph over uneven ground. From launching to landing, the projectile was in the air for a total of 3.5s. Neglect air resistance in your calculations and show your work. 55 million 1000m ilk myth In It ) Tom = 24.5972 m/s =V; Gone (cos-d Part A) 25% Find the displacement of the projectile from launching to landing. Provide your answer in unit vector notation and SI units. AF = + å ta tvit 9 - 9.8miga 0=25° Ve Vi=24,5972m/s +-3.5 - (-99) 4a +(vi cos@ C+ Visinoj]t - (Vicosot) C+ átgta : Vising t) Ì =(24.6 m/s ) cos 25%3.5j+ (-9.3ml?) (3.59464. Chinese s V = Vi Cosoit Visin o = 78m2 - 23. Can? Part B) 25% How fast is it moving when it hits the ground? P 32.7ms] Question 2: 25% Ve= ătt u Fl-99H+ +(Vicos e C+ Vi sin @jy (22.3)*+(23. Amon = (Vicosof? + (Visino-gt) ] = (24.6% 1s) cos 250 a + (24.6 15) sin 250 - 19.gm/s) (3.559 = 22.3 m/sê -23,9 m IF X = 31 – 21,] =-î + 3k, and Č = 53 +4ť, find 2Ă - (A+B x Ć). Show your work. Txuñ - 2A. A + BX C) = 2/37-25) [(37-25) + (-1 + 32 ) x (5] +46)] +2/37-23[(31-04)+ 47+3)x(59+4E)] Å xe = 7 (+ 1 + 3k) x(57 +48) -2/30-44. (30-29-5E-15t+47) -Sex} + 15 Rx7-42 + 12x =2(38-4) (-12? +27 - 5E) -2(13)(12) +taja) +(0)653) -21-40) More on back → E-80 -sexyte T 5

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Answer 1

here,

1)

the angle of launch , theta = 25 degree

the initial speed , u = 55 mph = 24.59 m/s

time interval , t = 3.5 s

the displacement in vertical direction , y = u * sin(theta) * t - 0.5 * g * t^2

y = 24.59 * sin(25) * 3.5 - 0.5 * 9.81 * 3.5^2 m

y = - 23.7 m

the displacement in horizontal direction , x = u * cos(theta) * t

x = 24.59 * cos(25) * 3.5 m = 78 m

the displacement = ( 78 m i - 23.7 m j)

b)

let the final speed be v

using conservation of energy

0.5 * m * v^2 = 0.5 * m * u^2 + m * g * y

v^2 = 24.59^2 + 2 * 9.81 * 23.7

v = 32.7 m/s

the final speed is 32.7 m/s

2)

r = 2 A . ( A + B X C)

r = 2 A . ( A + (- i + 3 k) X (5 j + 4 k))

r = 2 A . ( A + (- 5 k + 4 j - 15 i))

r = 2 A . ( (3 i - 2j) + (- 5 k + 4 j - 15 i))

r = 2 A . ( - 12 i + 2 j - 5k)

r = 2 (3 i - 2 j) . ( - 12 i + 2 j - 5k)

r = 2 * ( 3 * (-12) + (2) * (-2))

r = - 80 units