A plane dives at 37° to the horizontal and releases a package at an altitude of 380m. If the load is in the air for 4s, find:
a) the speed of the plane when it released the package;
b) the horizontal distance traveled by the package after it is released.
Vertical speed initial: -Vsin37
hf=hi+Vi*t-4.9t^2
0=380-Vsin37*t-4.9t^2 t is given at 4 seconds, solve for V.
horizontal distance:Vcos37*t
To solve this problem, we need to break it down into a few steps.
Step 1: Calculate the vertical velocity of the package when it is released.
To do this, we can use the formula for vertical velocity: v = u + gt
where v is the final vertical velocity, u is the initial vertical velocity, g is the acceleration due to gravity (approximately -9.8 m/s^2), and t is the time.
In this case, the package is dropped, so the initial vertical velocity is 0 m/s. The time is given as 4 seconds. Substituting these values into the equation, we get:
v = 0 + (-9.8) * 4 = -39.2 m/s
The negative sign indicates that the velocity is downward.
Step 2: Calculate the horizontal distance traveled by the package.
To do this, we can use the formula for horizontal distance: d = v * t
where d is the horizontal distance, v is the horizontal velocity, and t is the time.
In this case, the horizontal velocity is the same as the velocity of the plane when it released the package.
To find the horizontal velocity, we can use the formula: v = u * cos(theta)
where v is the horizontal velocity, u is the velocity of the plane, and theta is the angle between the plane's direction of motion and the horizontal.
In this case, the angle theta is given as 37 degrees. We need to convert this to radians to use in the formula. Since 180 degrees = pi radians, we have:
theta = 37 * pi / 180
Now we can substitute the given values into the formula to find the horizontal velocity:
v = u * cos(theta)
u = v / cos(theta) = -39.2 / cos(37 * pi / 180)
Step 3: Calculate the horizontal distance traveled by the package.
Substituting the known values into the formula for horizontal distance, we have:
d = v * t
d = (-39.2 / cos(37 * pi / 180)) * 4
Calculate this expression to find the horizontal distance traveled by the package.