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A rugby player runs with the ball directly toward his opponent’s goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball’s velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative to the field while he passes the ball with velocity
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Chapter 4 Solutions
FUNDAMENTALS OF PHYSICS - EXTENDED
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- You are operating a radio-controlled model car on a vacant tennis court. Your position is the origin oc coordinates, and the surface of the court lies in the xy-plane. The car, which we represent as a point, has x and y-coordinates that vary with time according to x = 2.0 m – (0.25 m/s2)t2 y = (1.0 m/s)t + (0.025 m/s3)t3 1. Find the car’s coordinate’s and distance from you at time t = 2.0 s. A) (1.0m, 2.2 m) r = 2.4 m B) (2.2m, 1.5m) r = 2.7m C) (2.5m, 2.05m) r = 3.2 m D) (2.3m, 1.0m) r = 2.5m 2. The components of the car’s instantaneous velocity are the time derivatives of the coordinates: vx = dx/dt = (-0.25 m/s2)(2t), vy = dy/dt = 1.0 m/s + (0.025 m/s3)(3t2) This can be expressed as velocity vector v = vxî + vyĵ = (-0.5 m/s2)tî + [1.0 m/s + (0.075 m/s3)t2]ĵ 3. What are the components of instantaneous velocity and its…arrow_forwardIf the vector components of the position of a particle moving in the xy plane as a function of time are x = (2.8 m/s2)t2 and y = (6.4 m/s3)t3, at what time t is the angle between the particle's velocity and the x axis equal to 45°?arrow_forwardAt time t = 0, the position vector of a particle moving in the x-y plane is r = 5.80i m. By time t = 0.016 s, its position vector has become (6.08i + 0.42j) m. Determine the magnitude vay of its average velocity during this interval and the angle made by the average velocity with the positive x-axis. Answers: m/s Vav 0= i iarrow_forward
- At time t = 0, the position vector of a particle moving in the x-y plane is r = 4.62i m. By time t = 0.011 s, its position vector has become (4.84i +0.54j) m. Determine the magnitude Vay of its average velocity during this interval and the angle 0 made by the average velocity with the positive x-axis. Answers: Vav 0= i i m/sarrow_forwardA space vehicle is coasting at a constant velocity of 24.4 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.223 m/s² in the +x direction. After 52.7 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction. (a) Number i Units (b) Number Units ûarrow_forwardThe coordinates of a particle moving in the XY plane are given as function of time by: X = 5m + ( 7 m/s^4) t^4 Y = ( 10 m/s)t + (3 m/s^5)t^5 a. Find the position vector of the body at t = 3.5 sec b. Find the instantaneous acceleration of the body at t = 3.5 sec c. Find the average velocity during the time interval from t 1 = 2 sec to t2 = 4.5 secarrow_forward
- A space vehicle is coasting at a constant velocity of 24.6 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.201 m/s² in the +x direction. After 47.8 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction. (a) Number i (b) Number i Units Units +arrow_forwardThe equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. π Then write the particle's velocity at t= as a product of its speed and direction. The velocity vector is v(t) = (i+j+ k.arrow_forwardA student standing on a cliff that is a vertical height d d = 25 ft above the level ground throws a stone with velocity v0 v 0 = 59 ft/s at an angle θ θ = 18 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position. With what speed, vfvf in feet per second, does the stone strike the groundarrow_forward
- A space vehicle is coasting at a constant velocity of 15.4 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.255 m/s² in the +x direction. After 45.7 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction. (a) Number i (b) Number i eTextbook and Media Hint Save for Later Units Units Attempts: 0 of 3 used Submit Answerarrow_forwardA space vehicle is coasting at a constant velocity of 17.8 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.280 m/s2 in the +x direction. After 33.6 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction.arrow_forwardA car is moving on a straight road in a fixed direction at a constant speed of v = 64 km/h with respect to the road. You wish to state the kinematic vectors of the motion of the car by using a Cartesian coordinate system whose positive x-axis is pointed in the direction of the motion of the car and the origin is fixed at some point on the road. Part (a) What is the expression for the velocity of the car, using the speed v and the unit vectors i, j, and k? Part (b) What is the x-component of the position vector, in units of kilometers, at time t = 0.035 hr?arrow_forward
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