An eagle dives from it's nest with a velocity of -81/3 feet per second. Find the vertical displacement in 4 1/2 seconds
To find the vertical displacement of the eagle in 4 1/2 seconds, we can use the equation of motion.
The equation of motion for vertical displacement with initial velocity, time, and acceleration is given by:
d = vt + (1/2)at^2
Where:
d is the vertical displacement
v is the initial velocity
t is the time
a is the acceleration
Given:
Initial velocity, v = -81/3 feet per second
Time, t = 4 1/2 seconds
We need to find the vertical displacement, d.
Step 1: Convert the mixed number time to an improper fraction.
4 1/2 = 9/2
Step 2: Substitute the given values into the equation of motion.
d = (-81/3)(9/2) + (1/2)(-32)(9/2)^2
Step 3: Simplify the equation.
d = (-27)(9/2) + (1/2)(-32)(81/4)
Step 4: Perform the calculations.
d = -243/2 + (-1296/4)
Step 5: Convert the fractions to a common denominator.
d = -243/2 - 1296/4
Step 6: Find a common denominator for the fractions.
d = -243/2 - 648/2
Step 7: Combine the fractions with a common denominator.
d = (-243 - 648)/2
Step 8: Add or subtract the numerators.
d = -891/2
Therefore, the vertical displacement of the eagle in 4 1/2 seconds is -891/2 feet.
To find the vertical displacement of the eagle, we need to calculate the distance it has traveled vertically in 4 1/2 seconds.
The formula to calculate the displacement is:
displacement = initial velocity * time + (1/2) * acceleration * time^2
In this case, the initial velocity is -81/3 ft/s, the time is 4.5 seconds, and the acceleration is due to gravity, which we can assume as -32 ft/s^2 (acceleration is negative because it acts downward).
Plugging these values into the formula, we get:
displacement = (-81/3) * 4.5 + (1/2) * (-32) * (4.5)^2
Now, let's simplify the equation and solve for the displacement:
displacement = -363/2 + (-16) * 20.25
displacement = -363/2 - 324
displacement = -363/2 - 648/2
displacement = (-363 - 648) / 2
displacement = -1011/2
Therefore, the vertical displacement of the eagle in 4 ½ seconds is -1011/2 ft.
assuming it dives vertically down, and gravity helps,
s(t) = -81/3 t - 16t^2
s(4.5) = -445.5 ft
If no gravity included, and the eagle flies at a constant velocity, just exclude that term
-81/3 * 9/2 = -121.5 ft
PS: why ever assign a speed of 81/3? That's just 27!
If you mean 8 1/3, then redo the calculation with the proper value (25/3).