4 You are to launch a rocket, from just above the ground, with one of the following initial velocity vectors: (1) v 20i + 70j, (2) Vo = -201 + 70j. (3) Vo = 20i - 70j. (4) Vo = -20i - 70j. In your coordinate system, x runs along level ground and y increases upward. (a) Rank the vectors according to the launch speed of the projectile, greatest first. (b) Rank the vectors according to the time of flight of the projectile, greatest first.
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- A particle travels along xyz – plane with an equation of motion given by v (t) = 9.20 t2 m i – 6.20 t3 m j + 4.10 t4 m k. g3 a. Determine the magnitude of the average velocity of the particle from t = 2.00 s to t – 5.00s . b. Determine the magnitude of the position vector when t = 4.00s .A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a 32° ramp, measured from the horizontal, at a speed of 40.0 m/s (144 km/h). The top of the ramp is at the same height as the roofs of the buses and each bus is 20.0 m long. A)How many buses does he clear? B) and how by how many meters does he clear the last bus?Your nephew got a Nerf Bazooka gun for Christmas, so you take it outside to play with it (just like my uncles did when I was little). The bazooka is on your shoulder, 1.5 m above the ground. You aim the gun 25° above the horizontal and the big, foam projectile leaves the gun with an initial velocity of 36 m You accidentally aim the bazooka at a tree that is a horizontal distance of 27 m away. How long does it take for the projectile to hit the tree? t = How high (above the ground) in the tree does the projectile get stuck? hfinal = m Imagine you were more clever and aimed into an empty field with no obstructions. You can control how fast the projectile leaves the gun by pumping more times or fewer times (more pumps = faster projectile). What are TWO ways you could increase the amount of time that the projectile is in the air?
- 9. You are a basketball player shooting a three-point shot. You are standing 10.0 m from the basket, which is 3.0m above the floor. You jump up and shoot the ball, releasing the ball when your hands are at the same height as the basket (3.0 m). You release the ball with an initial velocity va, at an angle 0 = 42° from the horizontal. The ball goes in! Your team wins! VA V=0, 3 m + distace 10 m a. What was the initial velocity of the ball? (Show your work, put a box around your answer.) Ax = 10m Ay=3M A=-9.0'0² V6+2(98) ( Vo 14m/3)X b. What maximum height above the FLOOR was reached by the ball? (Show your work, put a box around your answer.). V= Vo°+ 2A (A4) +219.8)(Y-0) O 14f -19.664-0 196 =19.6y = )8m 14 = Vot Vot use Vy acce krahom c. If you wanted to decrease the required initial velocity on the ball, would you increase or decrease the initial angle from the horizontal? Check one: increase the angle decrease the angle Version B 3. Page 6 of 8An object is propelled from the origin with acceleration ? =(4.00?̂+2.00?̂) ?/?2 and initial velocity ? 0 =(8.00?̂+12.0?̂) ?/? for 5.00 seconds. After this 5.00 second interval, the object then travels as a projectile. a. Determine how long the object is in the air. b. What is the object’s position vector (in unit-vector notation) when it reaches its maximum altitude? c. What is the object’s velocity vector (in magnitude and direction) just before it hits the ground?24. A shell is fired with a horizontal velocity in the positive x direction at a speed of 330 m/s from the top of an 80- m high cliff. The shell strikes the ground 1330 m from the base of the cliff. What is the magnitude of the velocity of the shell as it hits the ground? Hint: you need to determine horizontal and vertical components of the final velocity first, from the kinematic equations, then calculate magnitude of the velocity. While the horizontal velocity remains constant, the vertical velocity does not. You will need time of flight to determine the latter. 80 m 1330 m A) 4.0 m/s B) 9.8 m/s B) 9.8 m/s C) 82 m/s D) 170 m/s (E) 332 m/s