week 1 assignment - PHYS133

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Physics

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Dec 6, 2023

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Mariah Keller Castillo 5786597 PHYS133 K002

Chapter 1: problem 9 (a) To find the distance the tectonic plate moves in 1 second at a speed of 4.0 cm/year, you can use the following formula: Distance = Speed × Time Given: Speed = 4.0 cm/year Time = 1 second Convert the speed to cm/second: Speed = 4.0 cm/year × (1 year / 365 days) × (1 day / 24 hours) × (1 hour / 3600 seconds) Speed ≈ 4.0 / (365 × 24 × 3600) cm/second Now, plug the values into the formula: Distance = Speed × Time Distance ≈ (4.0 / (365 × 24 × 3600)) cm/second × 1 second Calculate the distance: Distance ≈ 1.27 × 10^ (-9) cm (b) To find the speed in kilometers per million years, you can use the following steps: Convert the speed from cm/year to km/million years: Speed = 4.0 cm/year × (1 km / 100000 cm) × (1000000 years / 1 million years) Speed ≈ 0.00004 km/million years So, the tectonic plate's speed is approximately 0.00004 kilometers per million years. Chapter 1: problem 12 The percent uncertainty can be calculated using the formula: Percent Uncertainty = (Uncertainty / Measurement) × 100%

Given: Uncertainty (Δx) = 0.50 cm Measurement (x) = 20 m = 2000 cm (since 1 m = 100 cm) Plug in the values into the formula: Percent Uncertainty = (0.50 cm / 2000 cm) × 100% Percent Uncertainty = 0.025 × 100% Percent Uncertainty = 2.5% So, the percent uncertainty of the measuring tape's measurement is 2.5%. Chapter 2: problem 6 (a) To calculate the average speed of the helicopter blade tip in the helicopter's frame of reference, you can use the formula for the circumference of a circle: Circumference = 2π × radius Given: Revolutions per minute = 100 Radius (r) = 5.00 m Convert revolutions per minute to revolutions per second: Revolutions per second = 100 revolutions/minute × (1 minute / 60 seconds) Revolutions per second = 5/3 revolutions/second Now, calculate the average speed: Average Speed = Circumference × Revolutions per second Average Speed = 2π × 5.00 m × 5/3 revolutions/second Calculate the average speed: Average Speed ≈ 52.36 m/s So, the average speed of the helicopter blade tip in the helicopter's frame of reference is approximately 52.36 meters per second. (b) The average velocity over one revolution will be zero because the blade returns to its starting point after one complete revolution. The displacement is zero, and thus the average velocity, which is displacement divided by time, becomes zero. Chapter 2: problem 19

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To calculate the average acceleration of the intercontinental ballistic missile, you can use the following formula: Average Acceleration = (Final Velocity - Initial Velocity) / Time Given: Initial Velocity (u) = 0 m/s (starting from rest) Final Velocity (v) = 6.50 km/s = 6500 m/s Time (t) = 60.0 s Average Acceleration = (6500 m/s - 0 m/s) / 60.0 s Average Acceleration ≈ 108.33 m/s² Now, let's express this acceleration in multiples of g: 1 g = 9.80 m/s² Average Acceleration in multiples of g = (Average Acceleration) / (1 g) Average Acceleration in multiples of g ≈ 108.33 m/s² / 9.80 m/s² Average Acceleration in multiples of g ≈ 11.05 g So, the average acceleration of the intercontinental ballistic missile is approximately 108.33 m/s² or about 11.05 times the acceleration due to gravity (g). Chapter 2: problem 25 Let's break down each part of the problem: (a) To calculate the distance the runner travels during deceleration over a certain time, you can use the following kinematic equation: Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2 Given: Initial Velocity (u) = 9.00 m/s Acceleration (a) = -2.00 m/s² (negative because it's deceleration) Time (t) = 5.00 s Plug in the values into the formula: Distance = 9.00 m/s × 5.00 s + (1/2) × (-2.00 m/s²) × (5.00 s)^2 Distance = 45.00 m - 25.00 m Distance = 20.00 m So, the runner travels 20.00 meters during the next 5.00 seconds of deceleration.

(b) To find the final velocity of the runner, you can use the following kinematic equation: Final Velocity = Initial Velocity + (Acceleration × Time) Given: Initial Velocity (u) = 9.00 m/s Acceleration (a) = -2.00 m/s² (negative for deceleration) Time (t) = 5.00 s Final Velocity = 9.00 m/s + (-2.00 m/s²) × 5.00 s Final Velocity = 9.00 m/s - 10.00 m/s Final Velocity = -1.00 m/s The negative sign indicates that the runner has reversed her direction and is moving backward at 1.00 m/s. (c) It's important to evaluate the result to make sure it makes sense. In part (a), the distance traveled during deceleration is positive, indicating that the runner moved forward in the opposite direction of her initial motion. In part (b), the negative final velocity confirms that the runner has changed her direction and is moving backward. The results make sense because the runner decelerated, meaning she slowed down and reversed her direction. This is reflected in the negative final velocity and the fact that the distance traveled is positive, showing her movement in the opposite direction.

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