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.
help please. thankyou.
vf=a*time
Vf=(-9.8m/s^2+3.80m/s^2)*2.45
are you sure? because this is a acceleration in two dimensions problems. the answer is supposed to be in the form of ( , )m/s.
To solve this problem, we can use the equations of motion for constant acceleration.
First, let's calculate the change in velocity caused by gravity. Since the electron starts at rest, the initial velocity in the y direction (vy) is 0. The acceleration in the y direction (ay) is given as -9.80 m/s^2. The time (t) is 2.45 s. We can use the following equation to find the change in velocity in the y direction (Δvy):
Δvy = ay * t
Δvy = -9.80 m/s^2 * 2.45 s = -23.96 m/s
Next, let's calculate the change in velocity caused by the electric field in the x direction. The initial velocity in the x direction (vx) is also 0. The acceleration in the x direction (ax) is given as 3.80 × 10^6 m/s^2. Using the same equation as before, we can find the change in velocity in the x direction (Δvx):
Δvx = ax * t
Δvx = 3.80 × 10^6 m/s^2 * 2.45 s = 9.31 × 10^6 m/s
Since the electron starts at rest, the initial velocity in both the x and y directions is 0. Therefore, the final velocity in the x direction (vfx) is equal to the change in velocity in the x direction (Δvx), and the final velocity in the y direction (vfy) is equal to the change in velocity in the y direction (Δvy).
Finally, we can calculate the magnitude and direction of the final velocity using the Pythagorean theorem:
vf = sqrt(vfx^2 + vfy^2)
vf = sqrt((9.31 × 10^6 m/s)^2 + (-23.96 m/s)^2)
vf = sqrt(8.669561 × 10^13 m^2/s^2 + 574.3216 m^2/s^2)
vf = sqrt(8.669561 × 10^13 m^2/s^2 + 574.3216 m^2/s^2)
vf ≈ sqrt(8.669561 × 10^13 m^2/s^2) ≈ 2.944 × 10^6 m/s
Therefore, the velocity of the electron 2.45 s after it starts to move is approximately 2.944 × 10^6 m/s, in a direction calculated from the angles of the electric field and the gravity.