A car comes to a stop over a distance of 30.0 m after the driver applies the breaks. If the car decelerates at a constant rate of 3.50 m/s 2, what was the car's original speed? 10.2 m/s

14.5 m/s

105 m/s

210 m/s

none of the above

During your summer internship for an aerospace company, you are asked to design a small research rocket. the rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 910 m above the earth's surface. the rocket's engines give the rocket an upward acceleration so it moves with acceleration of 16.0 m/s2 during the time t that they fire. after the engines shut off, the rocket is in free fall. ignore air resistance.

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.