airplane

[yankee]

A plane drops a hamper of medical supplies from a height of 3680m during a practice run over the ocean. The plane's horizontal velocity was 136 m/s at the instant the hamper was dropped. The acceleration of gravity is 9.8m/s^2. What is the magnitude of the overall velocity of the hamper at the instant it strikes the surface of the ocean? Answer in units of m/s.

Please help- I don't know where to start or what formla to use!

[kreil]

I'm pretty sure the speed of the plane is irrelevant since the hamper was dropped vertically and thus did not have an initial vertical velocity. Assuming this is correct, this is just a classic free-fall problem using the equation

v_f^2=v_i^2+2ad

Here d is the height, a is gravity, and vi is zero. Putting in these variables and then their values, the answer would be:

v_f=\sqrt{2gh}=\sqrt{(2)(9.8)(3680)}=268.6 \frac{m}{s}


Josh

[HallsofIvy]

kreil, I disagree. I don't see any way to drop something from an airplane, negating the horizontal speed of the airplane. The speed of the airplane is important since the hamper will have that initial horizontal speed. You have two equations: vertical acceleration is -9.8 so vertical speed is vy(t)= -9.8t and vertical height is y(t)= -4.9t2+ 3680. Set that equal to 0 and solve for t to find the time when the hamper hits the water. Use vy(t)= -9.8 t to find the horizontal velocity at that point.
Horizontal acceleration is 0 so the hamper will still have horizontal velocity 136 m/s when it hits the water. Use both horizontal and vertical velocities to find the "magnitude of the overall velocity of the hamper at the instant it strikes the surface of the ocean".