What is the velocity required to escape the earths

Question

Assignment:

1. A ball is thrown vertically upwards with a speed of 15 m/s from the ground. At the same instant of time a second ball is thrown vertically upwards with a speed vo from a height of 30 m above the first ball. If both land at the same time. what is the speed vo of the second ball.

A. 5.2 m/s

B. 15 m/s

C. 0.3 m/s

D. 10.1 m/s

2. A mass m is pushed down an incline, compressing a spring a distance d. When released find an expression for the speed the mass will reach when the spring is uncompressed. Assume the incline is frictionless.

A. v = √k/m d - 2gd

B. v = √k/md² - 2gd

C. v = √k/m d²

D. v = √k/m d² - 2gd sinθ

3. If a particular force has a potential enerp, U(x) = 9x² - 0.5x⁴. Find the force at a position x = 3m

A. (40.5 N) x

B. (56.7 N) x

C. (0 N) x

D. - (40. 5 N) x

4. What is the velocity required to escape the earths gravitational attraction. (Note: M_Earth = 5.97 x 10²⁴ kg and R_Earth = 6.37 x 10⁶m)

A. v_esc = 1.12 x 10⁴ m/s

B. v_esc = 7.91 x 10³ m/s

C. v_esc = 1.25 x 10⁸ m/s

D. v_esc = 19.6 m/s

5. A sphere a filled cylinder and a hollow cylinder of inner radius R/2, all with a mass M and radius R. If all three start from rest find the ratio of the speed of the sphere v_sphere  to the speed of the hollow v_cylinder

16. A mass in sitting on a frictionless table has an initial speed v_i. The mass is attached to a piece of string that is being acted on by a force F at the center. Find the speed v_f of the mass when the radius of the string decreases to r

A. v_f = v₀ (R/r)

B. v_f = m v_o R

C. v_f = v₀ (R/r)²

D. v_f = v₀ (r/R)