1. A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass, based on its size, of 5×109kg . It is approaching the Earth on a head-on course with a velocity of 810 m/s relative to the Earth and is now 5.5×106km away.With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?
Express your answer using two significant figures.
2. A ball of mass M and radius r1 on the end of a thin massless rod is rotated in a horizontal circle of radius R0 about an axis of rotation AB, as shown in the figure
a.Considering the mass of the ball to be concentrated at its center of mass, calculate its moment of inertia about AB.
b.Using the parallel-axis theorem and considering the finite radius of the ball, calculate the moment of inertia of the ball about AB
c.Calculate the percentage error introduced by the point mass approximation for r1 = 9.0 cm and R0 = 1.1 m .
3. The figure(Figure 1) illustrates an H2O molecule. The O-H bond length is 0.96 nm and the H-O-H bonds make an angle of 104 ° .
a. Calculate the moment of inertia for the H2O molecule about an axis passing through the center of the oxygen atom perpendicular to the plane of the molecule. Express your answer to two significant figures and include the appropriate units.
b.Calculate the moment of inertia for the H2O molecule about an axis passing through the center of the oxygen atom in the plane of the molecule, bisecting the H-O-H bonds. Express your answer to two significant figures and include the appropriate units
4. using what you've learned in this course, how many food calories would you burn by walking up the stairs for one hour? be sure to show your your work, state any assumptions or estimates and cite any information you had to look at.
b. look up a more realistic estimate for the number of calories that are burned by climbing stairs per hour. comment on any discerpancy