1. State whether the following are scalar or vector quantities: (a) A temperature of 50 °C (b) A downward force of 80N (c) 300J of work (d) A south-westerly wind of 15 knots (e) 70m distance (f) An acceleration of 25m/s2 at 30 to the horizontal
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- Write Newton’s Second Law of Motion for three-dimensionalmotion with only the gravitational force (acting in the z-direction).Find the work done by a force F of 12 pounds acting in the direction (3,1) in moving an object 8 feet from (0,0) to (8,0).6. A payload is launched from a plane at altitude 3000 meters with an initial horizontal and vertical velocity given by the vector m/s. Gravity pulls downward at 10 meters per second-squared. If the object encounters wind resistance proportional to velocity with , find the time and location from drop of the object's ground strike. [Use Excel to plot and estimate the time of impact.]
- A fish swimming in a horizontal plane has velocity V₁ = (4.00 i + 1.00 j) m/s at a point in the ocean where the position relative to a certain rock is = (14.0 i 3.60 j) m. After the fish swims with constant acceleration for 19.0 s, its velocity is = (17.0 13.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s² ay m/s2 (b) What is the direction of its acceleration with respect to unit vector î? counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = y = m m In what direction is it moving? counterclockwise from the +x-axisDetermine the magnitude and the direction of the resultant force measured counterclockwise from the positive x - axis.Find the work W done by a force of 77 pounds acting in the direction 30° to the horizontal in moving an object 8 feet from (0,0) to (8,0).
- A seasoned parachutist went for a skydiving trip where he performed freefall before deploying the parachute. According to Newton's Second Law of Motion, there are two forcës acting on the body of the parachutist, the forces of gravity (F,) and drag force due to air resistance (Fa) as shown in Figure 1. Fa = -cv ITM EUTM FUTM * UTM TM Fg= -mg x(t) UTM UT UTM /IM LTM UTM UTM TUIM UTM F UT GROUND Figure 1: Force acting on body of free-fall where x(t) is the position of the parachutist from the ground at given time, t is the time of fall calculated from the start of jump, m is the parachutist's mass, g is the gravitational acceleration, v is the velocity of the fall and c is the drag coefficient. The equation for the velocity and the position is given by the equations below: EUTM PUT v(t) = mg -et/m – 1) (Eq. 1.1) x(t) = x(0) – Where x(0) = 3200 m, m = 79.8 kg, g = 9.81m/s² and c = 6.6 kg/s. It was established that the critical position to deploy the parachutes is at 762 m from the ground…A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.Determine the work done by the constant force.
- A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 3.25 ✕ 10−5 T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration. HINT (a) the magnitude (in N) of the magnetic force acting on the ion N (b) the magnitude (in m/s2) of the ion's acceleration m/s24. A bullet is fired from ground level at a speed of 2200 feet per second at an angle of 30° from the horizontal. Find the magnitude of the horizontal and vertical components of the velocity vector. uith thọ horizontal, FindHow much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-N force at an angle of 30 degrees from the horizontal?