A 55.5-kg athlete leaps straight up into the air from a trampoline with an initial speed of 8.2 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? (b) Select the height at which the athlete's speed is 8.2 m/s as y = 0. What is her kinetic energy at this point? %3D What is the gravitational potential energy associated with the athlete? (c) What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete? (d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. m (e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/s

A sprinter who weighs 639 N runs the first 8.6 m of a race in 1.9 s, starting from rest and accelerating uniformly. What are the sprinter's (a)speed and (b) kinetic energy at the end of the 1.9 s? (c) What average power does the sprinter generate during the 1.9 s interval?

A 5.8 × 105 kg train is brought to a stop from a speed of 0.85 m/s in 0.57 m by a large spring bumper at the edge of its track.  What is the force constant k of the spring in N/m?

Timmy is sat down in class, looking around the room. He notices a water bottle on a desk next to him and thinks to himself that since the water bottle is on the desk it must not have kinetic energy. Is he right yes, or no? Explain?

A spring-loaded toy gun is used to launch a 10 g plastic ball.  The spring, which has a spring constant of 10N/m is compressed by 10 cm as the ball is pushed into the barrel.  When the trigger is pulled, the spring is released and shoots the ball back out horizontally.  a) What is the ball's speed as it leaves the barrel?  Assume the friction is negligible. b) If the toy gun was shot vertically upward, how high would the ball go?  Use energy concepts.

A 108 kg man is skiing across level ground at a speed of 9.5 m/s when he comes to the small slope 1.2 m higher than ground level shown in the following figure. -8.0 m- f1.2 m (a) If the skier coasts up the hill, what is his speed (in m/s) when he reaches the top plateau? Assume friction between the snow and skis is negligible. 8.16 m/s (b) What is his speed (in m/s) when he reaches the upper level if a 75 N frictional force acts on the skis? 6.31 X m/s

If object B also has 24 J of kinetic energy, is it moving faster or slower than object A? Find the ratio of the speeds of objects A and B. By what factor does the speed of each object change if total work -12 J is done on each?

Blocks 1 and 2, with masses m₁ and m2, are placed on a frictionless, horizontal table with an ideal spring between then. The blocks are moved together, compressing the spring until it stores 87 J of elastic potential energy. When released from rest, the blocks move in opposite directions. Find the maximum speed of block 1 if m₁ = 7.63 kg and m2 = 4.18 kg. m/s V =

Given: A shooting guard throws a basketball m = 1 kg straight up with an initial speed of v0 = 5.5 m/s. He releases the ball at shoulder height h0 = 1.95 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.  What is the height, hm in meters?

For a certain run, the following data is obtained when filling up Table 2 of the manual: Mass of cart = 600 g, hanging mass = 33 g, distance travelled by the cart = 49 cm, initial speed of the cart = 0.38 m/s, Final speed of the cart = 0.8 m/s, Calculate the percent difference between change in potential energy and change in Kinetic Energy.