1. If the initial height of the rock in Fig. 6-17 is y1 = h = 4.1-m calculate the rock's velocity when it has fallen to 1.7-m above the ground. 2. If the initial height of the rock in Fig. 6-17 is y1 = h = 4.7 calculate the rock's velocity when it has fallen to 2.5 m above the ground. 3. If you throw a 148.83 g baseball straight up into the air at 36.8-mph how high will it get if air resistance is not present??? 4. If you throw a 148.83 g baseball straight up into the air at 56.3-mph how high will it get if air resistance is not present??? 5. Assuming the height of the hill in Fig. 6-18 is 47 m, and the roller-coaster car starts from rest at the top, First: Calculate the speed of the roller-coaster car at the bottom of the hill (on your paper) Then answer: At what height will the coaster have 0.40 times its original speed. Take y = 0 at the bottom of the hill. 6. Assuming the height of the hill in Fig. 6-18 is 36 m, and the roller-coaster car starts from rest at the top, First: Calculate the speed of the roller-coaster car at the bottom of the hill (on your paper) Then answer: At what height will the coaster have 0.25 times its original speed. Take y = 0 at the bottom of the hill. 7. A dart of mass 0.100 kg is pressed against the spring of a toy dart gun as shown in Fig. 6-22a. The spring, with spring stiffness constant k = 277 N/m and ignorable mass, is compressed 6.6 cm and released. If the dart detaches from the spring when the spring reaches its natural length (x=0) what speed does the dart acquire? 8. A dart of mass 0.100 kg is pressed against the spring of a toy dart gun as shown in Fig. 6-22a. The spring, with spring stiffness constant k = 230 N/m and ignorable mass, is compressed 6.2 cm and released. If the dart detaches from the spring when the spring reaches its natural length (x=0) what speed does the dart acquire? 9. An ornament of mass 10.6 g is attached to a vertical ideal spring with a force constant (spring constant) of 42.3 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch? 10. (a) Determine the work a hiker must do on a 22.7-kg backpack to carry it up a hill of height h= 31.1 m, as shown in Fig. 6-4a. 11. A person pulls a 4.4-kg crate 40 m along a horizontal floor by a constant force FP = 116 N which acts at a 34 angle as shown in Fig. 6-3. The floor is rough and exerts a friction force FFR = 51 N Determine the work done by the friction force