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A: Given: H = 35 m Vi = 60 m/s ϴ = 250
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A: Answer 197.949m
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- A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69A bomber is flying at 300 mi/hr horizontally at an altitude of 2000 ft. Its target is a ship sailing at 15 mi/hr in theopposite direction and in the same vertical plane as the bomber. How far from the ship should the bomberrelease its bomb to score a direct hit? a. 5149.25 ft c. 4904.05 ftb. 1552.94 ft d. 2455.19 ftVectors u = −10i + 3j and v = −7i − 9j. What is u − v? a −17i − 6j b 17i + 6j c 3i − 12j d −3i + 12j
- 2. Two vectors are given by a = (4.0 m)i – (3.0 m)j+ (1.0 m)k and 6= (-1.0 m)î + (1.0 m)j+ (4.0 m)k. What is the (a) magnitude of a + 6? (b) In unit-vector notation, find: i. ā +5, ii. ā – 6, and iii. a third vector such that a -6+= 0 ?A ball is thrown at an initial height of 50 feet at an initial velocity of 65 feet/second at an angle of 75 degrees. Given the parametric equations y - 16t2 + Vo Sin(0)t + ho and x = Vo. Cos(0)t. When doing calculations, carry 5 digits of accuracy, so your round off does not build up. a. What is the ball's height in 2 seconds? 111.57035 v o feet. b. When will the object hit the ground? 4.60298 v o seconds. c. How far horizontally will the ball be when it hits the ground? 77.43702 v o feet. d. When will the ball be at its maximum height? 1.96204 o seconds. e. What is the ball's maximum height? 4.61479 x feet. feet f. How far horizontally will the ball be when it reaches its maximum height? 77.63571 ×1. Three vectors are given by, R = 2î + 3j – 6k, R2 = 21 – mj – 8k and R3 = nî + 4.5j – 9k Explain why R, & R2 are not parallel to each other. R || R3 & 2|R2 x R3| = [R, . (R2 × R3 )] + v58.8n, calculate the value of m. Calculate the angles that the vector (R, – R2) makes with î, ĵ & k axis. (b)
- A 238U nucleus is moving in the x direction at 5.0×105 m/s when it decays into an alpha particle (4He) and a 234Th nucleus. If the alpha particle moves off at 22 degrees above the x axis with a speed of 1.1×107 m/s, a) What is the speed of the thorium nucleus and b) What is the direction of the motion of the thorium nucleus ( degrees clockwise from the x axis)?Given that r (t) = (3t cos t)j – (3t sin t) k , is the position В. vector of a moving particle, find the following quantities: 1. The velocity, speed, acceleration, and curvature of the particle, 2. The tangential and normal components of acceleration of the particle. B.Let A⃗ =6î −4ĵ and B⃗ =−3î +7ĵ . What is C⃗ =A⃗ −4B⃗ ? Give your answer as a magnitude and direciton. Magnitude: Direction (specify as an angle measured counterclockwise from the positive x axis):
- Calculate vz, the x component of the velocity of the particle. Express your answer in meters per second.A bottle rocket is launched straight up. Its height in feet (y) above the ground x seconds after launch is modeled by the quadratic function: y = -16x2 + 124x + 8. How many seconds did it take the rocket to strike the ground? O 8.59 seconds o 7.814 seconds 7.31 seconds O 8.295 seconds b nb) I(1, 0, 0), J(0, 1, 0), and K(0, 0, 1) 6, A helicopter takes off at a ground velocity of 150 km/h. It climbs at an angle of 48° toward the east. A 17-km/h wind is blowing from the south. Determine the resultant air and ground velocities. Include a diagram in your solution. The Eiffel Tower is 324 m tall. Denise is