A rocket is fired vertically upward from the surface of the earth at a constant acceleration of 20.0 m/s2. After 30.0 s the fuel in the first stage of the rocket is expended, and the empty container is released and falls back to earth. Find the maximum height reached by the container.

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?

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1 kg projectile is launched at 30 m/sec, 60 degrees from horizontal. Find speed after 2 sec.

Dr. Jekyll (m = 70kg) is riding a skateboard when he realizes the cranberry juice he’s drinking is sweetened with artificial sweetener and turns into Mr. Hyde (m = 155kg). If Dr. Jekyll was initially moving at 6.5m/s, what is Mr. Hyde’s speed? (assume no external forces act)

Find the minimum initial speed of a projectile in order for it to reach a height of 2145 km above the surface of the earth

At a local swimming pool, the diving board is elevated h = 8.5 m above the pool's surface and overhangs the pool edge by L = 2 m. A diver runs horizontally along the diving board with a speed of v0 = 4.2 m/s and then falls into the pool. Neglect air resistance. Use a coordinate system with the horizontal x-axis pointing in the direction of the diver’s initial motion, and the vertical y-axis pointing up.  Determine the horizontal distance, dw in meters, from the edge of the pool to where the diver enters the water.

A block (mass = 5.56 kg) is released from rest at the top of a frictionless ramp. 1.01 seconds after release, the block has a speed of 6.34 m/s. Calculate the angle of the ramp in degrees as measured from the horizontal.

For physics equations, I always get confused on when little g should be negative or positive.  How do you determine when it should be or not?

At a local swimming pool, the diving board is elevated h = 8.5 m above the pool's surface and overhangs the pool edge by L = 2 m. A diver runs horizontally along the diving board with a speed of v0 = 4.2 m/s and then falls into the pool. Neglect air resistance. Use a coordinate system with the horizontal x-axis pointing in the direction of the diver’s initial motion, and the vertical y-axis pointing up. Calculate the time tw it takes the diver to fall off the end of the diving board to the pool's surface in terms tw in seconds.