An electron in a cathode-ray tube is traveling horizontally at 2.10×109 cm/s when deflection plates give it an upward acceleration of 5.40×1017 cm/s2 .How long does it take for the electron to cover a horizontal distance of 6.30 cm ?
What is its vertical displacement during this time?
To find the time it takes for the electron to cover a horizontal distance and its vertical displacement, we can use the kinematic equations of motion.
Let's start with the first part of the question, finding the time it takes for the electron to cover a horizontal distance of 6.30 cm.
1. Start with the equation:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
2. Rearrange the equation to solve for time:
Time = (sqrt((2 * Distance) / Acceleration)) - (Initial Velocity / Acceleration)
Plug in the given values:
Distance = 6.30 cm
Initial Velocity = 2.10×10^9 cm/s
Acceleration = 5.40×10^17 cm/s^2
Time = (sqrt((2 * 6.30) / 5.40×10^17)) - (2.10×10^9 / 5.40×10^17)
3. Calculate the time using a calculator:
Time ≈ 5.566 × 10^(-10) seconds
So, it takes approximately 5.566 × 10^(-10) seconds for the electron to cover a horizontal distance of 6.30 cm.
Now, let's move on to the second part of the question, finding the vertical displacement of the electron during this time.
1. Use the equation of motion for vertical displacement:
Displacement = Initial Velocity * Time + (1/2) * Acceleration * Time^2
Plug in the given values:
Initial Velocity = 0 (since the vertical velocity starts from rest)
Time = 5.566 × 10^(-10) seconds
Acceleration = 5.40×10^17 cm/s^2
Displacement = (1/2) * (5.40×10^17) * (5.566 × 10^(-10))^2
2. Calculate the vertical displacement using a calculator:
Displacement ≈ 8.303 × 10^(-19) cm
So, the electron has a vertical displacement of approximately 8.303 × 10^(-19) cm during the time it takes to cover a horizontal distance of 6.30 cm.