Finding Velocity of a Dropped Shellfish

[Aljazera]

Homework Statement

5. A sea hawk flying horizontally at a speed of 15 m/s drops a shellfish from a height of 30 m. At what speed does the shellfish hit the ground? Neglect air resistance (drag).

Homework Equations

vf2 = vi2 + 2ah

The Attempt at a Solution

I got 24.3 which was one of the answers and when i emailed the professor he said that that was the vertical velocity and I need to look for total velocity...well the answer is 28.5 m/s and I don't understand how that was arrived.

 

[rock.freak667]

You could use conservation of energy here I believe.


Also, the horizontal velocity would be the same throughout.

 

[nlightner]

I would approach this problem by first identifying the given information and the relevant equations. In this case, the given information is the initial velocity of the sea hawk, the height from which the shellfish was dropped, and the fact that air resistance can be neglected. The relevant equation is the kinematic equation vf2 = vi2 + 2ah, which relates final velocity (vf), initial velocity (vi), acceleration (a), and displacement (h).

Next, I would plug in the given values into the equation and solve for the final velocity:

vf2 = (0 m/s)2 + 2 (9.8 m/s2) (30 m)

vf2 = 588 m2/s2

vf = √588 m/s ≈ 24.2 m/s

This answer corresponds to the vertical velocity of the shellfish just before it hits the ground. However, the question asks for the total velocity at which the shellfish hits the ground. To find this, we can use the Pythagorean theorem, which states that the square of the hypotenuse (total velocity) is equal to the sum of the squares of the other two sides (vertical and horizontal velocities).

Therefore, the total velocity at which the shellfish hits the ground can be found by:

total velocity = √(vertical velocity2 + horizontal velocity2)

= √(24.2 m/s)2 + (15 m/s)2

= √(585.64 m2/s2 + 225 m2/s2)

= √810.64 m2/s2 ≈ 28.5 m/s

This is the total velocity at which the shellfish hits the ground, taking into account both the horizontal and vertical components of its motion.