A WNBA player tosses a basketball directly upward with an initial unknown velocity. 3 meters up in the air, the ball has a known velocity of 5 m/s upwards. 1) Using kinematic equations, determine the initial velocity of the ball. 2) Now using work and energy, determine the highest point which the ball reaches. Neglect air resistance. The acceleration due to gravity is 9.81 m/s^2.
1) The only equation we need to use for part 1 is: (Vf)^2 = (Vi)^2 + 2 * a * D, where: Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and D is the distance traveled. We know the final velocity after 3 meters have been traveled. Additionally, we can use gravity as the acceleration. However, we are using up as our positive vector, and gravity provides acceleration down, we must make the acceleration due to gravity negative. Plug those variables into the previous equation to get: (5 m/s)^2 = (Vi)^2 + 2 * ( -9.81 m/s^2) * (3 m), -solve for Vi - Vi = 9.15 m/s 2) Now that we found its initial velocity, we can find its highest point using work and energy equations. Recall that as an object falls down, its potential energy is converted into kinetic energy. The equations for energy that we need are: Potential Energy = m*g*h; where m is mass, g is gravity, and h is the change in height. Kinetic Energy = 0.5 * m * v^2, where v is the velocity. At the ball's highest point, there will be no kinetic energy. Thus, all of the initial kinetic energy is converted into potential energy. Even though we don't have the mass of the ball, we can still solve for the height. Potential Energy = Kinetic Energy => m*g*h = 0.5*m*v^2 -divide both sides by the mass=> g*h = 0.5*v^2. We know the acceleration due to gravity and the velocity at its lowest point (which we found in part 1). In this case, we do not need to make the acceleration due to gravity negative. We can plug those in and solve for 'h' (9.81 m/s^2) *h = 0.5*(9.15m/s)^2 h = 4.27 meters.
Jack and Jill both leave to school from separate houses at the same time. Jack lives 2 miles north of school, and Jill lives 5 miles south of Jack. If Jack decides to bike at a speed of 15 miles an hour, how fast would Jill have to bike in order to get there at the same time as Jack?
First, we notice that because Jill lives 5 miles south of Jack, and Jack lives 2 miles north of the school. This means that Jill lives 3 miles from school. 5 - 2 = 3 Now we have to calculate how long it takes Jack. We set up an equation as follows: 2 = 15 * time 15 is the speed, and 2 is the distance traveled. We know solve for the time by dividing both sides by 15: 2/15 = t; or t = .1333 hours. This is about of time that Jill has to spend biking. We set up a similar equation as before, except this time our unknown is our speed, and our distance has changed: 3 = speed * (.1333 or 2/15) Solving for the speed, we get our answer; speed = 22.5, which is in miles per hour
Which Galilean moon is a prime candidate for life? Why is that so?
There are four Galilean moons, and Europa is the one that scientists believe is the most likely to have life. This is because the key element for life, water, covers the surface of the moon in the form of ice. However, since Europa's orbit is small, the tidal forces of Jupiter may be strong enough to create a frictional force between the rocky core of the planet and its icy outside. The friction would cause heat, allowing for a liquid ocean to exist below the surface. http://solarsystem.nasa.gov/planets/europa/indepth