An object is dropped from an aircraft when it is directly above target...
Time taken to reach the ground = √(2H/g)
= √(2 � 1000 / 10)
= √(200)
= 10√2 seconds
Distance = Velocity � Time
= (500 � 5/18 m/s) � 10√2 s
= 1964.1 m
= 1.964 km
The bomb wil miss the target by distance of 1.964 km
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An object is dropped from an aircraft when it is directly above target...
Analysis:
To determine whether the object will hit the target or not, we need to consider the horizontal and vertical components separately.
Vertical Motion:
The object is dropped from a height of 1000m, which means its initial vertical velocity is 0 m/s. Assuming no air resistance, the only force acting on the object is gravity, which causes it to accelerate downwards at a rate of 9.8 m/s^2.
Using the equation of motion: h = ut + (1/2)gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can find the time it takes for the object to reach the ground.
Substituting the values, we have:
1000 = 0 * t + (1/2) * (9.8) * t^2
1000 = 4.9t^2
t^2 = 1000/4.9
t^2 ≈ 204.08
t ≈ √(204.08)
t ≈ 14.28 seconds
Horizontal Motion:
The horizontal velocity of the aircraft is given as 500 km/hr, which needs to be converted to m/s for consistency. We know that 1 km/hr is equal to 0.2778 m/s.
Therefore, the horizontal velocity of the aircraft is:
500 km/hr * 0.2778 m/s = 138.9 m/s
Since there are no horizontal forces acting on the object, its horizontal velocity remains constant throughout its motion. Therefore, the horizontal distance covered by the object is given by the equation: distance = velocity * time.
Substituting the values, we have:
distance = 138.9 m/s * 14.28 s
distance ≈ 1982.29 meters
Conclusion:
The object will miss the target by a distance of approximately 1982.29 meters. This is because while the object is in free fall, it also moves horizontally at a constant velocity. The time it takes for the object to reach the ground is the same as the time it takes for the aircraft to cover a horizontal distance of 1982.29 meters. Therefore, when the object hits the ground, it will be 1982.29 meters away from the target.
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