A plane drops a hamper of medical supplies

Question

A plane drops a hamper of medical supplies
from a height of 3080 m during a practice run
over the ocean. The plane’s horizontal velocity
was 135 m/s at the instant the hamper
was dropped.
What is the magnitude of the overall velocity
of the hamper at the instant it strikes
the surface of the ocean? The acceleration of
gravity is 9.8 m/s
2
.
Answer in units of m/s.

Answer 1

I would first find separately the horizontal and vertical velocities.

 

v_x = 135 m/s  [constant]

 

Get v_y at the bottom from kinematics.

 

v_y² - 0² = 2gh = 2(9.8)(3080) (m/s)² = 60368 (m/s)²

 

v_y = -245.7 m/s  [negative sign means going down]

 

v = √(v_x² + v_y²) = √[(135)² + (-245.7)²] m/s = 280.3 m/s

 

Its direction is 

 

tan^-1(v_y/v_x) = tan^-1(-245.7/135) = -61.2º,

 

i.e. 61.2º below the horizontal.

 

Note:

 

You could also get v_y from

 

3080 = 4.9t²

t = 25.07

v_y = -gt = -9.8(25.07) m/s = -245.7 m/s