Mechanics | Relativity Answers

A wave is described by the following equation:
y = (1.0 nm) sin 2π[t/.01s-x/2cm]

(i) Calculate the time period and the wavelength of the wave.

(ii) Obtain the expression for the velocity of the particles.

(iii) Calculate the speed of the particles at x = 3.0 cm, 5.0 cm and 7.0 cm at t = 0.01 s.

(iv) Calculate speed of the particles at x = 1.0 cm, at t = 0.011 s, 0.012 s and 0.013s.

A sail boat has initial coordinates (Xa ya) = (1000m,200m). Four minutes later it has a cooordinate (Xb Yb). Calculate&
(a) Components&
(b) The magnitude&
(c) the direction of the average velocity of the sailboat for the 4 mintime interval.

A fire fighter, 50.0 m away from a building ,directs a stream of water from a firehouse at an angle of 30 degrees above the horizontal as in the figure below. If the initial speed of the stream is 40m/s, at what height does the water strike the building?

When a girl on a swing reaches the lowest point, what will her tangential velocity and radial acceleration be? or will it be tangential acceleration and radial velocity?

The velocity of an 11-kg box changes from 5.1 m/s to 15 m/s. How much total work is done on the box?

A child of mass 30 kg skates down from the top of a ramp having a constant slope of 15°. The child’s speed increases from 1.5 ms−1 to 3.0 ms−1 as she reaches the bottom of the ramp. A force of kinetic friction of magnitude 50 N opposes her motion. Determine the length of the ramp. Take g = 10 ms−2.

A juggler throws a ball with an initial horizontal velocity of +1.1 m/s and an initial vertical velocity of +5.7 m/s. What is its acceleration at the top of its flight path? Make sure to consider the sign when responding. Consider the upward direction as positive

A simple pendulum has a period of 3.6 s. What is its length? Answer in meters.

It is the year 2305 and the tallest structure in the world has an insane height of 3.19×106 m above the surface of the Earth. A pendulum clock that keeps perfect time on the surface of the Earth is placed at the top of the tower. How long does the clock take to register one elapsed hour? The radius of the Earth is 6.38×106 m and its mass is 5.97×1024 kg. Answer in minutes.

You need to know the height of a room, but you have no tape measure. You fasten one end of a string to the ceiling of the room, and tie a small rock at the other end so it almost touches the floor. You start this simple pendulum swinging slightly, and measure its period, which is 3.50 seconds. How tall is the room? Answer in meters.