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Practice Problem Set 1

# Practice Problem Set 1 - b What is the runner’s...

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KNES300 Practice Problem Set 1 Dr. Timothy Judkins For the given pairs of vectors a v , solve for the following (assume x and: a) b a v v + , give magnitude and direction (in degrees) b) b a v v , give magnitude and direction (in degrees) c) b a v v d) b a v v × , specify if the vector points into or out of the paper 1. j i a v v v 5 3 + = , j i b v v v 1 2 + = 2. ( ) 2 , 3 = a v , ( ) 9 , 4 = b v 3. 4 = x a , 4 = y a , 5 = x b , 9 = y b 4. Magnitude of a is 5, direction of a is -30 degrees Magnitude of b is 7, direction of b is -15 degrees 5. ( ) ° = 90 , 2 a v , ( ) ° = 45 , 3 b v 6. ( ) rad 1 , 2 = a v , ( ) rad , 5 π = b v 7. Vector a : r =5, θ =140º Vector b : r =10, θ =-170º 8. 1 = r a , 2 / π θ = a , 2 = x b , 3 = y b Solve the following problems. 9. Find the length of a 90º arc with a radius of 2 m. 10. A runner runs counterclockwise around a circular track. The length of the track from start to finish (around the track and back to the start) is 400 m. The runner completes one lap in 60 sec (assume constant speed). a. What is the runner’s displacement when the runner reaches a distance of 200 m?
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Unformatted text preview: b. What is the runner’s instantaneous speed at 30 sec? c. What is the runner’s instantaneous velocity at 30 sec? d. Is the runner accelerating at any time? If so, when and what direction? 11. An athlete throws a javelin while running with a horizontal velocity of 20 m/s. The athlete throws the javelin with a velocity of 50 m/s (with respect to himself) at an angle of 30 degrees with respect to the ground. a. What is the true velocity of the javelin at the instant it leaves the athlete’s hand? b. What is the vertical and horizontal velocity of the javelin after 2 sec? c. What is the speed of the javelin at the instant it leaves the athlete’s hand? d. What is the speed of the javelin after 2 sec? x y...
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