Question

A driver coasts down a hill 200 m high with initial speed vo 35 m/s. The road has friction that results in a negative work -1.7 x 10° J. The effect of this is that the total initial energy is reduced by this amount by the time the car reaches the bottom of the hill. Calculate the speed of the car when it reaches the bottom of the hill. The mass of driver and passenger is 1750 kg 59.3 m/s 62.8 m 6) A 2,000-kg sailboat experiences an eastward force of 3000 N by the ocean tide and a wind force against its sails with magnitude of 6000 N directed 55° north of west as shown in the diagram below. Calculate the resultant acceleration of the sailboat Fw 6000 N Ft 3000 N 2000 kg

Answer 1

From conservation of energy w_f + mgh + 1/2 mv_0^2 = 1/2 mv_f^2 -1.7 times 10^6 + 1750 times 9.81 times 200 + 1/2 times 1750 times 35^2 = 1/2 times 1750 times v_f^2 v_f = 56.6 m/s Nearest value v_f = 56.1 m/s F^vector = F_t^vector + F_w^vector ma^vector = 3000 i^^-6000 cos 55 degrees i^^+ 6000 sin 55 degrees j^^a^vector = 1/2000 [-441.6 i^^+ 4914.9 j^^] Magnitude a = 2.5 m/s^2