Exercise 1.29 Vector A⃗ has y-component Ay = +17.0 m . A⃗ makes an angle of 38.0 ∘ counterclockwise from the +y-axis Part A What is the x-component of A⃗ ? Express your answer with the appropriate units. Part B What is the magnitude of A⃗ ? Express your answer with the appropriate units Exercise 2.48 A large boulder is ejected vertically upward from a volcano with an initial speed of 40.8 m/s . Air resistance may be ignored Part A At what time after being ejected is the boulder moving at a speed 19.2 m/s upward? Part B At what time is it moving at a speed 19.2 m/s downward? Part C When is the displacement of the boulder from its initial position zero? Part D When is the velocity of the boulder zero? Part E What is the magnitude of the acceleration while the boulder is moving? Part F What is the direction of the acceleration while the boulder is moving? up down Problem 2.69 The acceleration of a particle is given by ax(t)=− 2.10 m/s2 +( 2.95 m/s3 )t. Part A Find the initial velocity v0x such that the particle will have the same x-coordinate at time t= 4.06 s as it had at t=0. Part B What will be the velocity at time t = 4.06 s ? Exercise 2 Problem 2.68 An object's velocity is measured to be vx(t)=α−βt2, where α=4.00m/sand β=2.00m/s3 At t=0 the object is at x=0 Part A Calculate the object's position as a function of time. Part B Calculate the object's acceleration as a function of time. Exercise 15.6 A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.5 s fo crests are spaced 5.4 m apart. 1)How fast are the waves traveling? Express your answer with the appropriate units. 2)What is the amplitude of each wave? Express your answer with the appropriate units 3)If the total vertical distance traveled by the boat were 0.40 m , but the other data remained the same, how fast are the waves tr Express your answer with the appropriate units. 4)If the total vertical distance traveled by the boat were 0.40 m , but the other data remained the same, what is the amplitude of e Express your answer with the appropriate units. Exercise 15.22 A piano wire with mass m and length L is stretched with a tension of T. A wave with frequency f and amplitude A travels along th Part A Find an expression for the average power carried by the wave in terms of given quantities and any constants you may need Part B What happens to the average power if the wave amplitude is halved? What happens to the average power if the wave amplitude is halved? It will increase by a factor of 2. It will remain the same. It will decrease by a factor of 1/2. It will decrease by a factor of 1/4. The position of a squirrel running in a park is given by r⃗ =[(0.280m/s)t+(0.0360m/s2)t2]i^+ (0.0190m/s3)t3j^. A) What is , the -component of the velocity of the squirrel, as function of time? vx(t)=0.280m/s vx(t)=(0.280m/s)t+(0.0720m/s2)t2 vx(t)=0.280m/s+(0.0720m/s2)t vx(t)=(0.0720m/s2)t B) What is υy(t), the y-component of the velocity of the squirrel, as function of time? vy(t)=(0.0570m/s2)t2 vy(t)=(0.0570m/s3)t2 vy(t)=(0.0570m/s3)t+(0.0720m/s2)t2 vy(t)=(0.0570m/s3)t C) At 5.46 s , how far is the squirrel from its initial position? Express your answer to three significant figures and include the appropriate units. D) At 5.46 s , what is the magnitude of the squirrel's velocity? Express your answer to three significant figures and include the appropriate units. E) At 5.46 s , what is the direction (in degrees counterclockwise from +x-axis) of the squirrel's velocity? Express your answer to three significant figures and include the appropriate units 3.13 During a storm, a car traveling on a level horizontal road comes upon a bridge that has washed out. The driver must get to the other side, so he decides to try leaping the river with his car. The side of the road the car is on is h1 meters above the river, while the opposite side is lower and only h2 meters above the river. The river itself is a raging torrent x meters wide. Part A How fast should the car be traveling at the time it leaves the road in order just to clear the river and land safely on the opposite side? (enter an expression) 3.26 A model of a helicopter rotor has four blades, each of length 3.10 m from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 600 rev/min Part A What is the linear speed of the blade tip? Part B What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravity, g? 3.68 A firefighting crew uses a water cannon that shoots water at 30.0 m/s at a fixed angle of 53.0 ∘ above the horizontal. The firefighters want to direct the water at a blaze that is 15.0 m above ground level. Part A How far from the building should they position their cannon? There are two possibilities (d1
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