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An aeroplane moving horizontally at a sp...

An aeroplane moving horizontally at a speed of `200 m//s` and at a height of `8.0 xx 10^(3)m` is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released

A

9124 m

B

8714 m

C

8000 m

D

7234 m

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of determining the horizontal distance from the target at which the bomb should be released, we can follow these steps: ### Step 1: Identify the given values - Speed of the airplane (horizontal velocity, \( v_x \)) = 200 m/s - Height of the airplane (vertical distance, \( h \)) = \( 8.0 \times 10^3 \) m = 8000 m - Acceleration due to gravity ( \( g \)) = 10 m/s² (approximately) ### Step 2: Calculate the time taken for the bomb to fall The time \( t \) taken for the bomb to fall from the height \( h \) can be calculated using the second equation of motion for vertical motion: \[ h = \frac{1}{2} g t^2 \] Rearranging the equation to solve for \( t \): \[ t^2 = \frac{2h}{g} \] Substituting the values of \( h \) and \( g \): \[ t^2 = \frac{2 \times 8000}{10} = \frac{16000}{10} = 1600 \] Taking the square root: \[ t = \sqrt{1600} = 40 \text{ seconds} \] ### Step 3: Calculate the horizontal distance traveled during this time The horizontal distance \( d \) traveled by the bomb while it is falling can be calculated using the formula: \[ d = v_x \times t \] Substituting the known values: \[ d = 200 \, \text{m/s} \times 40 \, \text{s} = 8000 \, \text{m} \] ### Conclusion The bomb should be released at a horizontal distance of **8000 meters** from the target.
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