A highway curves to the left with radius of curvature of 36 m and is banked at 28 ◦ so that cars can take this curve at higher speeds. Consider a car of mass 1717 kg whose tires have a static friction coefficient 0.87 against the pavement. top view R = 36 m 28 ◦ rear view µ = 0.87 How fast can the car take this curve without skidding to the outside of the curve? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.

Suppose that a cylindrical tank 6 meters high with a radius of 2 meters is filled to the rim with water. the tank is buried so that the top of the tank is 1 meter below ground level. the space above the tank is not filled with water. calculate how much work needs to be done by a pump to pump the water out of the tank up to ground level. (the water weighs 9,800 newtons per cubic meter.)

Derive the formula 2as=v² -u² where the formula have have usual meanings