Concept explainers
(a)
The magnitude of the velocity of the parasailer as a function of time.
Answer to Problem 11.164P
Explanation of Solution
Given information:
Length of rope is defined as,
Constant velocity of the boat is
The angle is increasing at
The velocity in radial and transverse components,
The acceleration in radial and transverse components,
Calculation:
According to given information,
Convert,
We know that,
Therefore,
According to the explanation, the relative velocity of parasailer with respect to boat is,
The relative co-ordinates of the relative velocity is equal to,
Therefore the velocity of parasailer is equal to,
We can rewrite this as,
Where,
To find the magnitude,
Now, plot the graph,
Conclusion:
The magnitude of velocity of the parasailer is equal to,
The relevant graph is shown above.
(b)
The magnitude of acceleration of parasailer at
Answer to Problem 11.164P
Explanation of Solution
Given information:
Length of rope is defined as,
Constant velocity of the boat is
The angle is increasing at
The velocity in radial and transverse components,
The acceleration in radial and transverse components,
Calculation:
According to given information,
Convert,
We know that,
Therefore,
According to the explanation, the relative acceleration of parasailer with respect to boat is,
The acceleration of parasailer is equal to,
At,
Therefore the magnitude is equal to,
Conclusion:
The magnitude of acceleration of the parasailer is equal to,
Want to see more full solutions like this?
Chapter 11 Solutions
Vector Mechanics For Engineers
- A car moved on a horizontal path from rest at constant acceleration from point A until it reached its maximum speed when passing by At point b it took 4 seconds, and after point B it continued its movement but at a slowdown of -3 m / s2 until it stopped at c Categorical The idling distance of 13.5 m. Find: 1. The distance the car traveled while accelerating from a to b 2. The car's rate of acceleration (acceleration) 3. The car's maximum speed from point b 4. The time the car took when slowing down from b to carrow_forwardA satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to g(R/r)2, where g= 9.81 m/s2, R= radius of the earth = 6370 km, and r = distance from the center of the earth to the satellite. Assuming that the orbit of the moon is a circle with a radius of 384 × 103 km, determine the speed of the moon relative to the earth.arrow_forwardAn accelerometer record for the motion of a given part of a mechanism is approximated by an arc of a parabola for 0.2 s and a straight line for the next 0.2 s as shown in the figure. Knowing that v = 0 when t= 0 and x= 0.8 ft when t= 0.4 s, (a) construct the v-t curve for 0 ≤ t≤ 0.4 s, (b) determine the position of the part at t= 0.3 s and t= 0.2 s.arrow_forward
- 1.a Determine the Velocity of Cable at Point C. Note: Block E is moving downward with a velocity of 4m/s. 1.b Determine the Velocity of block W. Note: Block E is moving downward with a velocity of 4m/s. 1.c Determine the Relative Velocity of Point C with respect to Block E. Note: Block E is moving downward with a velocity of 4m/s. 1.d Determine the Relative Velocity of Block W with respect to Block E. Note: Block E is moving downward with a velocity of 4m/s. 2.a Determine the acceleration of rope at Point A and block B. Note: The block b is lifted 4 inches & velocity at 2ft/s. 2.b Determine the acceleration of block B. Note: The block b is lifted 4 inches & velocity at 2ft/s. 2.c After 0.5 seconds. Determine the velocity of the handle/cable A. Note: The block b is lifted 4 inches & velocity at 2ft/s. 2.d After 0.5 seconds. Determine the change in position of the handle/cable A. Note: The block b is lifted 4 inches & velocity at 2ft/s.arrow_forwardAt the instant under consideration, the hydraulic cylinder AB has a length L = 0.75 m, and this length is momentarily increasing at a constant rate of 0.2 m∕s. If vA = 0.6 m∕s and ? = 35°, find the rate of change of the length L in m/s, in order for the velocity of the slider B to be 0.15 m/s.arrow_forwardA car is about to pass through an arc bridge, as shown in the figure below. Given that ?௫ =5 m/s, determine the magnitude and direction of the car’s acceleration at the highest point, B, and at the endof the bridge, point C (assume the car is still on the bridge)arrow_forward
- A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot bumper system. After the coupling, the motion of the car is defined by the relation x = 60e - 4.8t sin 16t, where x and t are expressed in millimeters and seconds, respectively. Determine the position, the velocity, and the acceleration of the railroad car when (a) t= 0, (b) t = 0.3 s.arrow_forward.a Determine the Velocity of Cable at Point C. Note: Block E is moving downward with a velocity of 4m/s. 1.b Determine the Velocity of block W. Note: Block E is moving downward with a velocity of 4m/s. 1.c Determine the Relative Velocity of Point C with respect to Block E. Note: Block E is moving downward with a velocity of 4m/s. 1.d Determine the Relative Velocity of Block W with respect to Block E. Note: Block E is moving downward with a velocity of 4m/s.arrow_forwardQuestion 8 A car is traveling around a circular track of 680-ft radius. If the magnitude of its total acceleration is 9.5 ft/sec2 at the instant when its speed is 40 mi/hr, determine the rate at at which the car is changing its speed.arrow_forward
- A car A is travelling along a straight path, while a lorry B is travelling along a circular path having a radius of curvature of 200 m as shown in Figure Q3. At the instant shown, car A travel at the velocity of (150+2) km/h while lorry B travel at the velocity of 80 km/h. Also at this instant, car A has an increase velocity of 7000 km/h2 and lorry B has a decrease velocity of 4500 km/h2. The angle between straight path of car A and the horizontal line is θ=65°. Calculate the magnitude and direction of velocity of lorry B with respect to car A. Determine the magnitude and direction of acceleration of lorry B as measured by the driver of car A.arrow_forward7. Two cars are traveling around identical circular circuits. A car A travels at a constant speed of 20 m / s. Car B starts at rest and accelerates with constant tangential acceleration until its speed is 40 m / s. When car B has the same (tangential) speed as car A, it is always true that: choose an asnwer A-)it is passed to car A. B-)which has the same linear (tangential) acceleration as car A. C-)which has the same centripetal acceleration as car A. D-)which has the same total acceleration as car A .. E-)which has traveled further than the car A from the start.arrow_forwardA satellite will travel indefinitely in a circular orbit around a planet if the normal component of the acceleration of the satellite is equal to g(R/r)2, where g is the acceleration of gravity at the surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Knowing that the diameter of the sun is 1.39 Gm and that the acceleration of gravity at its surface is 274 m/s2, determine the radius of the orbit of the indicated planet around the sun assuming that the orbit is circular.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY