1. The river is 104 m wide. There is a current flowing at a velocity of 1.8 m/s [E]. You try to swim across the river going due North, you typically swim at a speed of 1.2 m/s in still water. Once you reach the other side, how far downstream would the current have pushed you, in meters?
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- David is buying a jet boat this summer and spending a lot of time zooming around. One place he plans on going is to the Plate River above Albany, NY. The current is 4 m/s south and the river is 200m wide. the boat will move at 20 m/s at full throttle, his only setting. A. how quickly will he cross the river if he heads straight across?B. how far downstream will he end up if he does so?C. if he wants to go straight across, what angle upstream should he use?Two trains are 900.0 kilometers apart. One is in Portland. The other is in San Francisco. They both begin traveling toward each other at the same time. The Portland train travels with an average velocity of 80.0 km/hr South. The San Francisco train travels North with an average velocity of 65.0 km/hr North.a. At what time will the two trains meet?b. How far away will they be from Portland when they meet?Question 4 A stretched string of length 50 cm is plucked a quarter of the way along its length to give an initial velocity of 10 m/s. Find expressions for the coefficients an and bn. a. an = 0 bn = 0 -0.5 b. an = 0.25 y(x,0) sin(kx)dx, b₁ = 0 4 0.5 = c. an = 0, bn foy(x,0) sin(kx) dx @n 4 -0.5 d. an = So y(x,0) sin(kx) dx, y(x,0)sin(kx)dx Wn b₁ =0.255 0
- a. Find the velocity v(t) and acceleration a(t). b. At what value of t does v=0? c. What is the maximum height?1. You are driving at 8.00 m/s south. You accelerate uniformly at 1.10 m/s? north for 5.00 seconds. How fast are you going at the end of the 5.00 seconds? What is your displacement?A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v⃗ =[ 5.00m/s − (0.0180m/s3) t2 ] i + [ 2.00m/s + (0.550m/s2) t ] j . a. What is the magnitude of the velocity of the car at t = 8.00 s? b. What is the direction (in degrees counterclockwise from + x-axis) of the velocity of the car at t = 8.00 s? c. What is the magnitude of the acceleration of the car at t = 8.00 s? d. What is the direction (in degrees counterclockwise from + x-axis) of the acceleration of the car at t = 8.00 s?
- 1. A rocket has an initial displacement of 1867 meters from the launchpad. It is moving with a velocity of 26 meters per second^2. What is it's displacement and velocity at t=200 seconds? 2. If this rocket has a jerk of 1 meter per second^3, then what is it's displacement at t=200 seconds? 3. If the rocket were traveling at an elevation angle (i.e., 0 degrees is horizontal and 90 degrees is vertical) of 30 degrees, then what is its horizontal displacement and its vertical displacement in meters?1) A man flies a small airplane from Fargo to Bismarck, North Dakota—a distance of 180 mi. Because he is flying into a head wind, the trip takes him 2 h. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15 min. What is his speed in still air, and how fast is the wind blowing? a. what is the speed (mph) in still air? b. wind speed (mph)? 2)A boat on a river travels downstream between two points, 60 mi apart, in 1 h. The return trip against the current takes 2 1/2 hours. a. What is the boat's speed (in still water)? b. How fast does the current river flow?