A swimmer who can consistently keep the same pace to cover 50 meters in 6.8 seconds sets out to swim across a river. The current in the river moves at 3.2 meters per second as the swimmer keeps a constant pace trying to get directly across (at a right angle to the current).

The river runs straight north-south with a current 4mph south. You paddle straight from west to east and your paddling speed is 3mph. Determine your actual speed and direction on a compass. (0 degrees is north, 90 degrees is east, etc.)

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Please help me answer number 5 with complete solution

In downtown Chicago, the east-west blocks are 400 ft long while the north-south blocks are 280 ft long. Because of the many one-way streets, it can be challenging to get around. Veronica starts at the corner of Dearborn and Ohio Streets. She drives four blocks north to Superior, two blocks east to Wabash, then a block south to get to her destination at Wabash and Huron. What is the straight-line distance from her starting point?

In a time of 2.67 h, a bird flies a distance of 86.7 km in a direction 30.2 degrees east of north. Take north to be the positive y direction and east to be the positive x direction. Express your answers in km/h. What is the x component of the bird’s average velocity?  What is the y component of the bird’s average velocity?

A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only a single nonzero component in the direction of motion. Thus, in this problem, we will call the velocity and a the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion, respectively. Figure U₁(m/s) 2.0 1.5 1.0 0.5 1(s) 0 10 20 30 40 50 1 of 1 (Figure 1) is a plot of velocity versus time for a particle that travels along a straight line with a varying velocity. Refer to this plot to answer the following questions. Part A What is the initial velocity of the particle, vo? Express your answer in meters per second. ▸ View Available Hint(s) V₁ =…

You drive 5.50 km in a straight line in a direction 25° East of North. (a) Find the distances you would have to drive straight East and then straight North to arrive at the same point. (This is equivalent to finding the components of the displacement along the East and North directions.) km East km North(b) Show that you still arrive at the same point if the East and North legs are reversed in order.

A hot air balloon is moving vertically upwards at a constant rate of 9.0 m/s. As the balloon rises, a package is dropped from the balloon and it takes 5 s to hit the ground. How far did the package fall?   Make sure to include a diagram of the physical situation, label know and unknown quantities with units, coordinate system. Please use grade 12 kinematics and label the variables as v1, v2, a (Acceleration), t (time), d (displacement) Thanks!

The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/s