An aeroplane moving horizontally at a speed of 200 m/s and at a height of 8.0×10 3 m is to drop a bomb on a target. At what horizontal distance from the target should the bomb be releasedA7.234kmB8.081kmC8.714kmD9.124km
Question
An aeroplane moving horizontally at a speed of 200 m/s and at a height of 8.0×10 3 m is to drop a bomb on a target. At what horizontal distance from the target should the bomb be releasedA7.234kmB8.081kmC8.714kmD9.124km
Solution
To solve this problem, we need to find the time it takes for the bomb to hit the ground after it's dropped from the plane, and then use that time to find the horizontal distance the bomb travels while falling.
Step 1: Find the time it takes for the bomb to hit the ground.
We can use the equation of motion: h = 0.5gt^2, where h is the height, g is the acceleration due to gravity, and t is the time.
Given that h = 8.0×10^3 m and g = 9.8 m/s^2, we can solve for t:
8.0×10^3 = 0.5 * 9.8 * t^2 t^2 = (8.0×10^3 * 2) / 9.8 t^2 = 1632.65 t = sqrt(1632.65) t = 40.41 seconds
Step 2: Find the horizontal distance the bomb travels while falling.
We can use the equation d = vt, where d is the distance, v is the velocity, and t is the time.
Given that v = 200 m/s and t = 40.41 seconds, we can solve for d:
d = 200 * 40.41 d = 8082 m or 8.082 km
So, the bomb should be released at a horizontal distance of 8.082 km from the target. The closest answer is B) 8.081 km.
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