You ride in a boat on a river flowing at 1.7m/s(in the negative y direction). Suppose you would like the boat to move directly across the river (in the positive x direction) with a speed of 5.5m/s.What is the corresponding direction of the boat's velocity relative to the water (i.e. from the positive x direction)?Express your answer to two significant figures and include appropriate units.

Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 3. a(t) = 8i + 4k v(0) = 5j, r(0) = 0 v(t) = r(t) = r(3) =

Johnny comes across a river that is 252 meters wide. He sees that the water flows eastward with a uniform velocity of 1.10m/s. Johnny sees his friend Sarah start her boat at point A on the south bank and start to cross the river to point B which is on the other side. Suppose the trip takes 3 minutes. Figure out the velocity of sarah's boat with respect to a) Johnny who is stationary on the ground b) A floating goose that's moving with the water. N B W-E S Vriver = 1.1 m/s A 252 m

Two-dimensional motion: Object A has a position as a function of time given by rA(t) = (3.00 m/s)t i + (1.00 m/s2)t2j. Object B has a position as a function of time given by r p(t) = (4.00 m/s)ti + (-1.00 m/s2)t2i. All quantities are SI units. What is the distance between object A and object B at timet= 3.00 s?

A rocket is shot straight up in the air from the ground at a rate of 46 feet per second. The rocket is tracked by a rangefinder that is 427 feet from the launch pad. Let d represent the distance from the rocket to the rangefinder and t represent the time, in seconds, since "blastoff". Express d as a function of t.

Problem 2: Kinematics and vectors. An object is moving on the xy plane with velocities given by: V₂ x = (10.0-0.500t)1 and v = (-5.00t+0.025²) j Determine the following quantities: a. The displacement of the object as a function of time. b. The average velocity of the object from for the time interval from 0 to 10 s.

Some troublemaking kids are dropping water balloons from the roof of your apartment building. You are in your fifth-floor room and your window is 25 m above the sidewalk outside. You look outside and see that each balloon hits the pavement 1.5 s after passing your window. Express answers using 2 significant figures. a) How fast are the balloons traveling when they pass your window? b) Assuming the balloons are being released from rest, from what height above your window are they being released? c) If you threw a balloon upwards from your window with an initial speed of 6.5 m/s, would you be able to get it to the roof?

A particle's position is given by  z(t) = −(7.30 m/s2)t2  for  t ≥ 0.  (Express your answer in vector form.) (a) Find the particle's velocity at  t = 2.50 s  and  t = 3.25 s. (b) What is the particle's average velocity during the time interval from  t = 2.50 s  to  t = 3.25 s?

Wyle E. Coyote hears a constant “Beep! Beep!” from around the corner of a cliff. Thinking it might be the Road Runner, he scampers up to speed and runs towards the sound to the East. On coming around the corner, he sees that it is not the Road Runner, but a truck coming towards him towards the West. The speed of the truck is 25 m/s. The speed of the Coyote is 100 m/s. The Coyote hears a frequency of 5500 Hz. The temperature of the air is 300 K. The mass of the truck is 1500 kg. The mass of the Coyote is 90 kg. Assume the air is an ideal gas with γ = 1.40 and the air molecules have a mass of 4.8*10-26 kg. The Boltzmann constant is k = 1.38*10-23 J/K. a. What is the speed of sound in this air? b. What is the original frequency of the horn on the truck? c. Assuming a perfectly inelastic collision, what is the final speed and direction of the truck, Coyote conglomerate (ignore any friction with the road)?

Moving sidewalks are installed every other 50 meters along the entire stretch of an airport walkway. These sidewalks move at a constant speed of 1 m/s. A lady passenger takes one of the sidewalks to go from one point to the next. If the passenger decides to go back using the same sidewalk at 1 m/s, how long will it take to reach her point of origin?