An electron starts at rest. Gravity accelerates the electron in the negative y direction at 9.80 m/s2 while an electric field accelerates it in the positive x direction at 3.80×106 m/s2. Find its velocity 2.45 s after it starts to move.
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To find the velocity of the electron after 2.45 seconds, we can use the equations of motion.
First, let's find the velocity component in the y-direction. The electron is accelerated by gravity in the negative y-direction at 9.80 m/s^2. Since the initial velocity is 0 m/s, we can use the equation:
v_y = u_y + a_y * t
where v_y is the final velocity in the y-direction, u_y is the initial velocity in the y-direction (which is 0 m/s), a_y is the acceleration in the y-direction (-9.80 m/s^2), and t is the time (2.45 s).
v_y = 0 + (-9.80) * 2.45
v_y = -23.98 m/s (velocity in the negative y-direction)
Next, let's find the velocity component in the x-direction. The electron is accelerated by an electric field in the positive x-direction at 3.80x10^6 m/s^2. Again, the initial velocity is 0 m/s, so we can use the same equation:
v_x = u_x + a_x * t
where v_x is the final velocity in the x-direction, u_x is the initial velocity in the x-direction (which is 0 m/s), a_x is the acceleration in the x-direction (3.80x10^6 m/s^2), and t is the time (2.45 s).
v_x = 0 + (3.80x10^6) * 2.45
v_x = 9.31x10^6 m/s (velocity in the positive x-direction)
Now, let's combine the velocities in the x and y-directions to find the resultant velocity. Since the motion is happening in a two-dimensional plane, we can use the Pythagorean theorem:
v = sqrt(v_x^2 + v_y^2)
where v is the resultant velocity.
v = sqrt((9.31x10^6)^2 + (-23.98)^2)
v = sqrt(8.6806x10^13 + 575.6804)
v = sqrt(8.6806x10^13 + 575.6804)
v = sqrt(8.6806x10^13)
v = 2.947x10^7 m/s (resultant velocity of the electron after 2.45 seconds)