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klemol [59]
3 years ago
15

It’s a sunny Saturday afternoon and you are walking around the lake by your house, enjoying the last few days of summer. The sid

ewalk surrounding the perimeter of the circular lake is crowded with walkers and runners. You then notice a runner approaching you wearing a T-shirt with writing on it. You read the first two lines, but are unable to read the third line before he passes. You wonder, ”Hmmm, if he continues around the lake, I bet I’ll see him again but I should anticipate the time when we’ll pass again.”
You look at your watch and it is 5:07pm. You estimate your walking speed at 3 m/s and the runner’s speed to be about 14 m/s. You also estimate that the diameter of the lake is about 2
miles. At what time should you expect to read the last line of the t-shirt?
Physics
1 answer:
Citrus2011 [14]3 years ago
7 0

The anticipated time when he will appear again is 5:17 pm

The given parameters;

your speed, V_a = 3 m/s

the runner's speed, V_b = 14 m/s

the diameter of the lake, d = 2 miles = 3218.69 meters

  • Let the anticipated time when he will appear again = t

The circumference of the lake is calculated as;

C = \pi d\\\\C = 3.142 \times 3218.69 = 10,113.12 \ m

Apply concept of relative velocity to determine the time, in which he will appear again.

By the time he appears again;

the distance you moved + distance he moved = circumference of the circle

V_at + V_bt = 10, 113.12\\\\(V_a + V_b)t = 10,113.12\\\\(3 + 14) t = 10,113.12\\\\17t = 10,113.12\\\\t = \frac{10,113.12}{17} \\\\t = 594.89 \ s = 9.92 \ \min \ \approx 10 \ \min

t\  \approx \ \ 5:17 \ pm

Thus, the anticipated time when he will appear again is 5:17 pm

Learn more here: brainly.com/question/20662992

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The time interval for which the proton remains in the field is -

Δt = $\frac{\pi R}{40}.

We have a proton entering a uniform magnetic field which is in a direction perpendicular to the proton's velocity.

We have to determine time interval during which the proton is in the field.

<h3>What is the magnitude of force on the charged particle moving in a uniform magnetic field?</h3>

The magnitude of force on the charged particle moving in a uniform magnetic field is given by -

F = qvB sinθ



According to the question, we have -

Entering Velocity (v) = 20 i  m/s

Magnetic field intensity (B) = 0.3 T

Leaving velocity (u) = - 20 j  m/s

Now -

The entering and leaving velocity vectors have 90 degrees difference between them. Therefore, only a quarter of distance of the complete circular path of radius 'R' is traced by the proton. Therefore -

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Since, the radius of circular path is not given, we will assume it R.

Therefore, time for which proton remained in the field is -

t = $\frac{\pi R}{2v} = \frac{\pi R}{40}

Hence, the time interval for which the proton remains in the field is -

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To solve more questions on Force on charged particle, visit the link below-

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