How to Calculate the Motion of a Dropped Fish in a Projectile Problem

[IronManTable]

Homework Statement

A sea bird catches a fish and then flies in an easterly direction with a speed v=7.39 m/s, h = 4.69 m above the surface of the sea. The fish has a mass of 115.3 g and is still alive. It thrashes and wiggles and as a result the bird drops the fish.

i) What is the speed of the fish when the bird drops it?

ii) What is the speed of the fish when it hits the water?

iii) When the fish hits the water it is momentarily stunned. It comes to a rest in 0.111 s. What is the magnitude of the force experienced by the fish as it comes to rest?

iv) How far horizontally from where it was dropped does the fish hit the water?

Homework Equations

v² = u² +2gh
v₂² = v₁² + 2ad
s = ut + 0.5 x t²
F = ma

The Attempt at a Solution

i) What is the speed of the fish when the bird drops it?

Since v₁ = 0
v₂² = v₁² + 2ad
v₂ = √(2ad)
v₂ = √(2 x 9.8 x 4.69)
v₂ = 9.59 m/s

ii) What is the speed of the fish when it hits the water?
Using Pythagoras' Theorem,
a² + b² = c²
∴ c = √(7.39² + 9.59²)
c = 12.1 m/s

iii) When the fish hits the water it is momentarily stunned. It comes to a rest in 0.111 s. What is the magnitude of the force experienced by the fish as it comes to rest?
s = ut + 0.5 x t²
4.69 = 0 + 0.5 x a x 0.111²
a = 4.69 / (0.5 x 0.111²)
a = 761.3 m/s²
F = ma
F = 0.1153 x 761.3
F = 87.8 N

iv) How far horizontally from where it was dropped does the fish hit the water?

I can't seem to figure out a way to get this answer. Can someone please check if my answers are right and can give me an insight on how to answer this last question? Thank you!​

 

[NascentOxygen]

[noparse]

(i) the speed of the fish at the moment the bird opens its talons;
(ii) you have applied the correct method, though answer can't be right.
(iii) wrong. Its movement in water is what takes 0.111s.[/noparse]

 

[IronManTable]

So how can I do the ones I got incorrect?

 

[NascentOxygen]

So how can I do the ones I got incorrect?

Try (i) again.

 

[IronManTable]

Okay well I tried it in a new foruma: v² = v₀² + 2a_y(y - y₀)

v² = v₀² + 2a_y(y - y₀)
v² = 0 + 2(-9.8)(0 - 4.69)
v² = 91.924
v = 9.59 m/s

I come up with the same answer?

 

[ehild]

The fish in the beak of the bird travels horizontally with the speed of the bird, and keeps that horizontal velocity component during its downward fall. The velocity has both horizontal and vertical components...ehild

 

[NascentOxygen]

Okay well I tried it in a new foruma: v² = v₀² + 2a_y(y - y₀)

v² = v₀² + 2a_y(y - y₀)
v² = 0 + 2(-9.8)(0 - 4.69)
v² = 91.924
v = 9.59 m/s

I come up with the same answer?

You have just calculated the fish's vertical speed after it has fallen to the water. But that is not what part (i) is asking.

This part of the question asks what is the speed of the fish before it starts to fall.

 

[IronManTable]

Oh! I get it now. It would be the same speed as the bird, correct? So, 7.39 m/s ?

 

[NascentOxygen]

Oh! I get it now. It would be the same speed as the bird, correct? So, 7.39 m/s ?

Right.

Now you have the right data values to do (ii).

 

[IronManTable]

Great! I've done (ii) and (iii) and managed to get the correct values. However, i can't seem to get the final one.

 

[ehild]

The motion of the fish is the resultant of a horizontal motion and a vertical one - it moves like a projectile.

ehild

 

[CWatters]

Hint: With projectile problems there is usually one parameter that is the same for both the horizontal and vertical motion and that is time. The horizontal and vertical velocities may well be different but the object usually starts and stops it's motion in both planes at the same time.