A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density p 3.06 x 106 g/m³ and volume V = 3.32 x 1012 m³. Recall that the universal gravitational constant is G : 6.67 x 10-11 N-m²/kg².

For years, the tallest tower in the United States was the Phoenix Shot Tower in Baltimore, Maryland. The shot tower was used from 1828 to1892 to make lead shot for pistols and rifles and molded shot for cannons and other instruments of warfare. Molten lead was dropped from the top of the 82.15 m tall tower into a vat of water. During its free fall, the lead would form a perfectly spherical droplet and solidify. Determine the velocity of the droplet right before it hits the ground. (Note: acceleration = -9.81 m/s/s) (Hint: think about the direction the droplet travels when considering its displacement.) ___________m/s

An 20.g bullet is fired from a rifle having a barrel 0.50 m long. Choosing the origin to be at the location where the bullet begins to move, then the force (in newtons) exerted by the expanding gas on the bullet is given by: F(x) = 1.7.10^3N + (1.0.10^2 N/m) x - (2.610^3 N/m^2)x^2 where x is in meters. Find the speed of the bullet as it leaves the barrel.

If a particle of mass 100 g initially had a speed of 100 cm/s, what would be its approximate kinetic energy at the end of its 10 cm fall? The correct answer is 15 x 10⁵ ergs

In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?

About 70 g of blood is pumped from a person's heart into the aorta during each heartbeat. The blood starts at rest with respect to the body and has a speed of about 1.2 m/s in the aorta. If the pumping takes 0.15 s, what is the magnitude of the average force exerted by the heart on the blood?

Two sticky spheres are suspended from light ropes of length L that are attached to the ceiling at a common point. Sphere A has mass 2m and is hanging at rest with its rope vertical. Sphere B has mass m and is held so that its rope makes an angle with the vertical that puts B a vertical height H above A. Sphere B is released from rest and swings down, collides with sphere A, and sticks to it. In terms of H, what is the maximum height above the original position of A reached by the combined spheres after their collision?

How to solve?

(a) A spaceship is projected vertically upward from the Earth's surface with an initial speed of 5.51 km/s, but unfortunately does not have a great enough speed to escape Earth's gravity. What maximum height does the spaceship reach (in m)? Ignore air resistance. 1.549e6 x Apply the conservation of mechanical energy, where v, = 0. You witt need to know the radius and mass of the Earth. Be careful with your signs when writing the potential energy expressions. Note that you can use energy conservation to write the initial potential energy of the system in terms of the escape velocity. Solve your equation for h. m initially at rest with (b) A meteorold falls from a height of 2.41 x 107 m above the surface of the Earth. What is the speed (in m/s) when the meteorite hits the Earth? Assume the meteoroid respect to the Earth. (Note that a meteorite is a meteorold that makes it to Earth's surface.) m/s

A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet.  a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.