Nate the skate was an avid physics student whose main non‑physics interest in life was high‑speed skateboarding. in particular, nate would often don a protective suit of bounce-tex, which he invented, and after working up a high speed on his skateboard, would collide with some object. in this way, he got a gut feel for the physical properties of collisions and succeeded in combining his two passions\.\* on one occasion, the skate, with a mass of 115 kg, including his armor, hurled himself against a 881 kg stationary statue of isaac newton in a perfectly elastic linear collision. as a result, isaac started moving at 1.67 m/s and nate bounced backward. what were nate\'s speeds immediately before and after the collision? (enter positive numbers.)

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.