In a TV set, an electron beam moves with horizontal velocity of 2.5 × 107 m/s across the cathode ray tube and strikes the screen, 44 cm away.
The acceleration of gravity is 9.8 m/s2 .
How far does the electron beam fall while traversing this distance?
Answer in units of m
time to get to screen:
time=distance/velocity
how far does it fall?
d=1/2 g t^2
To find the distance the electron beam falls while traversing this distance, we can use the equation for horizontal motion:
distance = horizontal velocity × time
First, we need to find the time it takes for the electron beam to traverse the 44 cm distance. Since we know the horizontal velocity of the beam (2.5 × 10^7 m/s), we can use this formula:
distance = speed × time
Rearranging the formula to solve for time, we get:
time = distance / speed
Converting the distance from centimeters to meters:
distance = 44 cm = 0.44 m
Plugging in the values:
time = 0.44 m / (2.5 × 10^7 m/s)
Calculating the time:
time ≈ 1.76 × 10^-8 s
Now, we can use this time to find the distance the electron beam falls. Since the acceleration due to gravity acts in the vertical direction, the formula for vertical motion is:
distance = acceleration × time^2 / 2
Plugging in the values:
distance = 9.8 m/s^2 × (1.76 × 10^-8 s)^2 / 2
Calculating the distance:
distance ≈ 1.68 × 10^-15 m
Therefore, the electron beam falls approximately 1.68 × 10^-15 m while traversing the 44 cm distance.
To find the distance the electron beam falls while traversing the given distance, we need to calculate the vertical distance the beam falls due to the acceleration of gravity.
First, let's calculate the time it takes for the electron beam to traverse the 44 cm distance horizontally. We can use the formula:
distance = velocity × time
Rearranging the formula to solve for time:
time = distance / velocity
Converting the distance to meters and using the given horizontal velocity of the electron beam:
distance = 44 cm = 0.44 m
velocity = 2.5 × 10^7 m/s
time = 0.44 m / (2.5 × 10^7 m/s)
Next, we can calculate the vertical distance the beam falls while traversing this time using the formula of motion under gravity:
distance = (1/2) × acceleration × time²
Given:
acceleration due to gravity = 9.8 m/s²
time = calculated in the previous step
Plugging in the values:
distance = (1/2) × 9.8 m/s² × (time)²
Now, let's calculate the value of time:
time = 0.44 m / (2.5 × 10^7 m/s) ≈ 1.76 × 10^-8 s
Plugging in the value of time:
distance = (1/2) × 9.8 m/s² × (1.76 × 10^-8 s)²
Calculating:
distance ≈ 1.36 × 10^-16 m
Therefore, the electron beam falls approximately 1.36 × 10^-16 meters while traversing the given distance.