A pelican flying along a horizontal path

[ArcherofScience]

a pelican flying along a horizontal path...

A pelican flying along a horizontal path drops a fish from a height of 5.4 m. The fish travels 8.0 m horizontally before it hits the watwe below. What was the pelican's initial speed?


Well I'm guessing that y =-5.4m and x= 8.0 m...what do I exactly do after...meaning how do I solve this?

 

[Doc Al]

How long does it take to fall 5.4 m? What kinematic equations describe the vertical motion?

 

[ArcherofScience]

Y=viy+at?

 

[Doc Al]

Y=viy+at?

No. Where did you get that equation? (Note that each term in that equation has different units, so it cannot possibly represent something real.)

Look here for a list of kinematic equations: Basic Equations of 1-D Kinematics

 

[Nickie]

To solve this problem, we will use the equation for projectile motion: y = y0 + v0y*t - 0.5*g*t^2, where y is the vertical distance, y0 is the initial height, v0y is the initial vertical velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.

In this case, y0 = -5.4 m, y = 0 m (since the fish hits the water at ground level), and x = 8.0 m. We can also assume that the initial horizontal velocity (v0x) is constant and does not affect the vertical motion.

Since the pelican drops the fish from a height of 5.4 m, we can use this to find the initial vertical velocity (v0y). Plugging in the values, we get:

0 = -5.4 m + v0y*t - 0.5*9.8 m/s^2*t^2

Solving for v0y, we get v0y = 8.2 m/s. This is the initial vertical velocity of the pelican when it drops the fish.

Now, to find the initial speed of the pelican, we can use the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the initial speed) is equal to the sum of the squares of the other two sides (in this case, v0x and v0y).

So, v0^2 = v0x^2 + v0y^2

Since we know v0y = 8.2 m/s and v0x is unknown, we can rearrange the equation to solve for v0x:

v0x = √(v0^2 - v0y^2)

Plugging in our known values, we get:

v0x = √(v0^2 - (8.2 m/s)^2)

Now, we need to find the value of v0. To do this, we can use the fact that the horizontal distance (x) traveled by the fish is equal to the horizontal component of the initial velocity (v0x) multiplied by the time (t). So, we can set up the equation:

x = v0x*t

Plugging in our known values, we get:

8.0 m = v