A helicopter is flying with a constant horizontal velocity of 144.2 kmph and is
directly above the point A when a loose part begins to fall. The part lands 6.5seconds later at point B on an inclined surface. Determine (a) The distance 'd'
between points A and B. (b) the initial height.
To solve this problem, we can break it down into two parts: the horizontal motion and the vertical motion.
(a) To determine the distance 'd' between points A and B:
Since the helicopter has a constant horizontal velocity, the horizontal distance traveled by the falling part can be calculated using the equation:
distance = velocity × time
Given that the horizontal velocity is 144.2 kmph and the time taken is 6.5 seconds, we need to convert the velocity to meters per second:
144.2 kmph = (144.2 × 1000) m/hr = (144.2 × 1000) / 3600 m/s = 40.06 m/s
Now, we can calculate the horizontal distance traveled:
distance = velocity × time
distance = 40.06 m/s × 6.5 s
distance ≈ 260.39 meters
Therefore, the distance 'd' between points A and B is approximately 260.39 meters.
(b) To determine the initial height:
To find the initial height at point A, we need to consider only the vertical motion of the falling part.
We can use the equation for vertical motion under constant acceleration:
distance = initial velocity × time + (1/2) × acceleration × time^2
In this case, the initial velocity is 0 m/s since the part starts falling from rest. The acceleration due to gravity is approximately 9.8 m/s^2.
distance = 0 × 6.5 + (1/2) × 9.8 × (6.5)^2
distance = (1/2) × 9.8 × (6.5)^2
distance ≈ 202.43 meters
Therefore, the initial height at point A is approximately 202.43 meters.
To solve this problem, we can break it down into two components: horizontal and vertical motion.
(a) To find the distance 'd' between points A and B, we need to determine the horizontal distance traveled by the helicopter in 6.5 seconds with a constant velocity of 144.2 km/h.
The horizontal distance can be calculated using the formula:
distance = velocity * time
Converting the velocity to meters per second:
144.2 km/h = 144.2 * (1000 m / 1 km) * (1 h / 3600 s) = 40.06 m/s
Now we can calculate the horizontal distance:
distance = 40.06 m/s * 6.5 s = 260.39 meters
Therefore, the distance 'd' between points A and B is 260.39 meters.
(b) To find the initial height, we need to consider the vertical motion of the falling part.
We can use the equation of motion:
h = ut + (1/2)gt^2
Where:
h = vertical displacement
u = initial vertical velocity (in this case, 0 since the object is falling)
g = acceleration due to gravity (-9.8 m/s^2)
t = time (6.5 seconds)
Plugging in the values, we get:
h = 0 + (1/2)(-9.8 m/s^2)(6.5 s)^2
= -1/2 * 9.8 m/s^2 * (6.5 s)^2
= -1/2 * 9.8 m/s^2 * 42.25 s^2
≈ -206.77 meters
The negative sign indicates that the object is falling, so the initial height is 206.77 meters below the starting point.
Therefore, the initial height is approximately 206.77 meters below point A.