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Homework 4 - Solutions

Homework 4 - Solutions - homework 04 FRENNEA KYLE Due 4:00...

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homework 04 – FRENNEA, KYLE – Due: Feb 13 2007, 4:00 am 1 Question 1 part 1 of 1 10 points A boat moves through the water of a river at 14 . 5 m / s relative to the water, regardless of the boat’s direction. If the current is flowing at 12 . 3 m / s, how long does it take the boat to complete a trip consisting of a 268 m displacement down- stream followed by a 196 m displacement up- stream? Correct answer: 99 . 0909 s (tolerance ± 1 %). Explanation: Let v b be the velocity of the boat relative to the water, and v w the velocity of water relative to the shore. Take downstream as the positive direction. For the downstream trip, the current is speeding him up, so the velocity of the boat relative to the shore is v d = v b + v w and the time is t d = x d v d = x d v b + v w For the upstream trip, the current is slowing him down, so the velocity of the boat relative to the shore is v u = v b v w and the time is t u = x u v u = x u v b v w The time for the entire trip is thus t = t d + t u = x d v b + v w + x u v b v w = (268 m) (14 . 5 m / s) + (12 . 3 m / s) + (196 m) (14 . 5 m / s) (12 . 3 m / s) = 99 . 0909 s Question 2 part 1 of 1 10 points A flashbulb is placed in the middle of a bus. When the flashbulb goes off, light from the bulb strikes the rear and front of the bus simultaneously, as seen by an observer, Karl, sitting in the bus. As seen by another observer, Fred, standing on the curb as the bus moves past, the light . 1. hits the front of the bus slightly before it hits the rear. 2. hits the front and back of the bus simul- taneously. 3. Not enough information to form a conclu- sion. 4. hits the rear of the bus slightly before it hits the front. correct Explanation: Both Karl and Fred observe the radiation moving at the same speed, but in Fred’s frame of reference, the rear of the bus moves to- ward the spot where the radiation was emitted while the front moves away, so the radiation reaches the rear of the bus first. Question 3 part 1 of 2 10 points A cheetah can run at a maximum speed 98 . 1 km / h and a gazelle can run at a maxi- mum speed of 71 . 1 km / h. If both animals are running at full speed, with the gazelle 66 . 4 m ahead, how long before the cheetah catches its prey? Correct answer: 8 . 85333 s (tolerance ± 1 %). Explanation: The relative velocity of the cheetah with re- spect to gazelle: Δ v = v ch v ga = 98 . 1 km / h 71 . 1 km / h = 27 km / h = 27 km / h × 1000 m / km 3600 s / h = 7 . 5 m / s

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homework 04 – FRENNEA, KYLE – Due: Feb 13 2007, 4:00 am 2 The relative distance which the cheetah has to cover is Δ x = 66 . 4 m. Then the time it takes the cheetah to catch the gazelle is : t = Δ x Δ v = 66 . 4 m 7 . 5 m / s = 8 . 85333 s Question 4 part 2 of 2 10 points The cheetah can maintain its maximum speed for only 7 . 5 s. What is the minimum distance the gazelle must be ahead of the cheetah to have a chance of escape? (After 7 . 5 s the speed of cheetah is less than that of the gazelle) Correct answer: 56 . 25 m (tolerance ± 1 %).
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