During the latter part of your European vacation, you are hanging out at the beach at the gold coast of Spain. As you are laying in your chaise lounge soaking up the warm Mediterranean sun, a large glob of seagull poop hits you in the face. Since you got an "A" in Physics you are able to estimate the impact velocity at 98.5 m/s. Neglecting air resistance, calculate how high up the seagull was flying when it pooped

Well, I guess you can come close, but you can't tell exactly.

It must be presumed that the seagull was flying through the air

when it "let fly" so to speak, so the jettisoned load of ballast

of which the bird unburdened itself had some initial horizontal

velocity.

That impact velocity of 98.5 m/s is actually the resultant of

the horizontal component ... unchanged since the package

was dispatched ... and the vertical component, which grew

all the way down in accordance with the behavior of gravity.

98.5 m/s = √ [ (horizontal component) ² + (vertical component) ² ].

The vertical component is easy; that's (9.8 m/s²) x (drop time).

Since we're looking for the altitude of launch, we can use the

formula for 'free-fall distance' as a function of acceleration and

time:

Height = (1/2) (acceleration) (time²).

If the impact velocity were comprised solely of its vertical

component, then the solution to the problem would be a

piece-o-cake.

Time = (98.5 m/s) / (9.81 m/s²) = 10.04 seconds

whence

Height = (1/2) (9.81) (10.04) ²

= (4.905 m/s²) x (100.8 sec²) = 494.43 meters.

As noted, this solution applies only if the gull were hovering with

no horizontal velocity, taking careful aim, and with malice in its

primitive brain, launching a remote attack on the rich American.

If the gull was flying at the time ... a reasonable assumption ... then

some part of the impact velocity was a horizontal component. That

implies that the vertical component is something less than 98.5 m/s,

and that the attack was launched from an altitude less than 494 m.