Sally puts a .1 kg golf ball on a spring that is 1-meter with the golf ball on it and is attached perpendicular to the floor the spring has a spring constant of 50 newtons per meter. Sally compresses the spring .5 meters and shoots the golf ball straight up. What is the max height of the golf ball?
We will solve this problem with kinetics instead of kinematics but either will work. When sally compressed the spring she adds potential energy to the system which is then transferred to kinetic energy in the golf ball and is returned to potential energy as the ball gets higher. To determine the max height we must examine the ball when its potential energy is at the maximum after the ball is launched. This will be when there is 0 spring potential energy and no ball kinetic energy. to determine the energy of the system we use the energy equation for a spring energy = .5 k x^2 meaning we have 6.25 joules or energy in the system. since all of this will be turned into potential energy when the ball is max height we set this value equal to the potential energy equations energy = m g h. m is given as .1 and g is 9.81 allowing us to solve for h as 6.4 meters lastly we can't forget to add the 1 meter the ball started at when it was on top of the spring giving us a max height of 7.4 meters above the ground
A hill has a sope that matches the function f(x) = 2x^3 -3(x)^2 -4x -6 sam wants to have a picnic on the hill but can not set up his tasty lunch anywhere on the hill where there is slope that is not perfectly flat or his lunch will fall down the hill. There may be other people on the hill so sam may need a backup plan if the first spot he tries is taken. Find x of 2 locations sam can set up his picnic
To find where there is no slope you must first take the derivative of the function as this will the function of the slope. f'(x) = 6x^2 -6x +4 next to find where there is no slope you set the derivative function equal to zero and solve for x: 0 = 6x^2 -6x -4 using the quadratic formula you can find the roots of the function to be x = 1/6 (3 - sqrt(33)) and x = 1/6 (3 + sqrt(33))
Every day Susan picks up her 8-year-old child from the school bus stop at 3:00 pm some days the bus arrives earlier and some days later. Today her child's bus still has not arrived and it is 3:16 she calls the school and they inform her that the bus arrival time has a population standard deviation is 8 minutes. Fearing that something might be the wrong Susan decides she will call the police if there is a 98% probability that the child's bus should have arrived. Should Susan call the police immediately or wait?
Susan should wait to call the police for another few minutes. Because the school told Susan the population standard deviation of the bus arrival times she should use a z table to determine the likely hood of the bus arriving before 3:16. To do this Susan must first find the z score by subtracting the sample by the mean and dividing by the standard deviation 16/8 = 2 giving Susan a z score of 2. looking up the probability of the arrival time being less than 2 z scores Susan can see that the probability of the bus arriving already is only .9772 and less than .98 so she would wait to call the cops