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a)If a electron projected horizontally with a speed of 3.0x10^9 m/s ,how far will it fall in traversing 1m of horizontal distance? Does the answer increase or decrease if the initial speed is increased?

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It's hard to read your handwritten equations, but intuitively the electron will fall less distance if it is traveling faster. In the same length of time it will fall the same amount; you are correct that the x and y dimensions are independent, as you have written y=0.5gt^2 . So you have a y in terms of t. Calculate how t increases or decreases for fixed x (1 meter) and variable speed v_x
Is this a trick question? The electron is projected at a speed that is faster than the speed of light?

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does this increase my score?

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