Sample Linear Kinetics Problems

1. A 70 kg runner has a vertical acceleration of 13.7 m/s² and a horizontal acceleration of 2.4 m/s². Draw a free body diagram and solve for the horizontal and vertical reaction forces. [R_x = 168 N,
R_y = 1645.7 N] The runner had an initial vertical velocity of -0.7 m/s and an initial horizontal velocity of 3.6 m/s. If the forces were applied over a period of 0.2 seconds, what are the runner's final vertical and horizontal velocities? [v_xf = 4.08 m/s, v_yf = 2.04 m/s]

2. How much force must be applied to a 0.5 kg ball traveling horizontally at 42 m/s to bring the ball to rest in 0.25 seconds? [F = -84 N]

3. A 110 kg University of Oregon football player runs into the goal post upright while attempting to catch a pass. If the Duck's initial horizontal velocity at the moment of impact was 9.3 m/s, and the impact lasts 0.2 seconds, what is the average force experienced while the Duck comes to rest?
[F = -5115 N]

4. A quarterback throws a 0.4 kg football from rest, resulting in a final velocity of 25 m/s at 25º. Determine horizontal and vertical components of the ball's velocity. [v_x = 22.7 m/s, v_y = 10.6 m/s] If the quarterback accelerates the ball for 0.15 seconds, determine the horizontal and vertical forces applied to the ball. [F_x = 60.4 N, F_y = 32.1 N] What is the magnitude and direction of the applied force?
[F = 68.4 N, q = 28.0º]

5. Horton the elephant's egg has a mass of 50 kg. The egg is thrown at you with a horizontal velocity of 10 m/s. How much impulse must you apply to bring the egg to rest? [Ft = -500 Ns]. Determine the force applied if the time of application is 0.1 seconds; 4 seconds. [F = -5000 N for 0.1 s; F = -125 N for 4 s]

6. A 70 kg sprinter applied a horizontal force to the ground of 1300 N for 0.2 seconds. After the force application, she has a final horizontal velocity of 9.7 m/s. What was her initial velocity? [v_i = 5.99 m/s]

7. After clearing the bar, a 75 kg high jumper has a vertical velocity of -1.7 m/s at a height of 1.25 m above the mat. Calculate potential, kinetic, and total energy, and peak height attained. [PE = 919.69 J, KE = 108.38 J, E = 1028.07 J, h = 1.4 m]

8. A weightlifter performs a maximum dead lift from rest for a distance of 0.98 m. She applied a force of 2200 N for 0.13 seconds to lift the 200 kg weight. What was the final vertical velocity of the weight? [v_yf = 0.15 m/s]

9. A weightlifter raises a 630 N barbell from 0.2 m to 1.8 m. Calculate the work done lifting the barbell. [W = 1008 J] If the lift was done in 0.38 seconds, how much power was generated? [P = 2652.5 Watts]

10. When landing from a vertical leap, a 549 N dancer decreases her vertical velocity from -5.9 m/s to -1.23 m/s, while lowering her center of mass a distance of 0.18 m. Calculate the work done and the average force absorbed by the dancer. [W = -1030.47 J, F = 5724.83 N]

11. Michael Jordan weighs 834 N. After completing one of his (once) famous slam dunks, he has a vertical velocity of -0.6 m/s at 1.4 m above the ground. Calculate his mass; potential, kinetic, and total energy; and maximum height attained. [m=85.02 kg, PE=1167.6 J, KE=15.3 J, E=1182.9 J, h=1.42 m]

12. An 82 kg runner experiences a horizontal reaction force of -1049.6 N and a vertical reaction force of 525.62 N. Determine the magnitude and direction of the resultant reaction force and acceleration, and the horizontal and vertical accelerations. [R=1173.9 N at 153.4°, a_x= -12.8 m/s², a_y= -3.4 m/s²,
a = 13.2 m/s² at 194.9°]

13. At the point of maximum depression of a diving board, a 50 kg diver has a vertical velocity of
-1.7 m/s and a height of 1.8 m. At the point of takeoff from the board, she has a height of 2.3 m and a vertical velocity of 3.8 m/s. Calculate work done from maximum depression to takeoff; potential, kinetic, and total energy at the moment of takeoff; and peak height attained. [W = 534 J, PE = 361 J,
KE = 1128.15 J, E = 1489.15 J, h = 3.04 m]