(14%) Problem 6: A football of mass m = 1 kg is thrown at an initial velocity of vo = 19 m/s at an angle of 0 = 31° with respect to the horizontal. The ball reaches a maximum height of h. Let gravitational potential energy be zero at ground level. (a) Give an expression for the initial velocity vector in rectangular form. Write your answer in terms of vo, 0, and the unit vectors i and j. (b) Write an expression for the potential energy, Ug, of the football at the peak of its trajectory, in terms of the variables given in the problem statement. Ug = (m vo Vo sin(0) sin(0) )/2 (c) How high did the ball travel, h, in meters?

A sledge loaded with bricks has a total mass of 18.6 kg and is pulled at constant speed by a rope inclined at 20.8° above the horizontal. The sledge moves a distance of 20.9 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. (a) What is the tension in the rope? (b) How much work is done by the rope on the sledge? kJ (c) What is the mechanical energy lost due to friction? kJ

A sledge loaded with bricks has a total mass of 18.8 kg and is pulled at constant speed by a rope inclined at 19.0° above the horizontal. The sledge moves a distance of 20.5 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. (a) What is the tension in the rope? N (b) How much work is done by the rope on the sledge? kJ (c) What is the mechanical energy lost due to friction? k]

A sledge loaded with bricks has a total mass of 18.1 kg and is pulled at constant speed by a rope inclined at 20.5° above the horizontal. The sledge moves a distance of 19.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. (a) What is the tension in the rope?N(b) How much work is done by the rope on the sledge?kJ(c) What is the mechanical energy lost due to friction?kJ

A roller coaster car with mass m and initial velocity v is at height h above the ground. Calculate the potential energy, kinetic energy and velocity for the following values:   h(m) m(kg) v(m/s) 1.00E+02 5.00E+02 0.00E+00

A point guard launches a basketball m = 1 kg straight up with an initial speed of v0 = 6.5 m/s. The ball leaves his hand at shoulder height h0 = 2.2 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g.

A 0.23-kg stone is held 1.5 m above the top edge a water well and then dropped into it. The well has a depth of 5.3 m. (a) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone-Earth system before the stone is released? J (b) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone-Earth system when it reaches the bottom of the well? J (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well? J