(b) A particle moves with position y = 2x , where x and y are in meters. The velocity in x direction is v, = 31² . Determine the velocity at time t = 5 s and write in unit vectors.

Problem 1: An object is thrown off the top of a 6.2-m tall building with a velocity of 2.9 m/s at an angle of 37° with respect to the horizontal. Part (a) How long is the object in the air in seconds? S sin() cos() tan() 7 8 9. НОME cotan() asin() acos() 4 6 atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END O Degrees O Radians CLEAR Part (b) What is the horizontal distance the object covers in meters?

A particle moves along a horizontal path with a velocity of v = (31²-61) m/s, where is the time in seconds. If it is initially located at the origin O, determine the distance traveled in 3.5 s, and the particle's average velocity and average speed during the time interval.

0, y 0) 44. A projectile is launched from the point (x QC with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance |r| from the ori- gin at the end of each second thereafter, for 0 s I S 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v and v will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to f, then r|must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain

Two airplanes leave an airport at the sametime. The velocity of the first airplane is680 m/h at a heading of 51.6◦. The velocityof the second is 640 m/h at a heading of 176◦.How far apart are they after 2.3 h?Answer in units of m.

A river is moving east at 5 m/s. A boat starts from the dock heading 40◦ south of east at 8 m/s. If the river is 2000 m wide, (a) what is the velocity of the boat with respect to Earth and (b) how long does it take the boat to cross the river?

Verify the ranges for the projectiles (a) forθ = 45º and the given initial velocities. Verify the ranges shown for the projectiles in Figure3.41(b) for an initial velocity of 50 m/s at the given initialangles

A drone is launched with a velocity of (55)m/s, (359). Three minutes after the drone is launched it suddenly changed its course to (48)m/s, (190) to avoid high trees on its way. Then, it finally goes back at a rate of (74)m/s, (153). Calculate for the total resultant vector of the drone. Pan am Flight 7 was one of the famous planes to disappear into the Bermuda Triangle, which is en route from San Francisco to Hawaii . The first route is due west for (687)km; then it took a detour southeast for (966)km; and the its final route is at 53° north of west, the crash site in the Pacific ocean, for (683) What is the plane’s total displacement? CIA and NSA launched a hiring program to new agents: to crack the safehouse of the nuclear launch codes. They were given hacking tools and random displacement as a starting point. Agent 1 is directed to (21)m, (316); Agent 2 is directed to (49)m, (47) and Agent 3 to (38)m due south. The three displacements lead to the point in the field where the key to…

(8%) Problem 1: A particle moves from point A to point B. Let L be the straight-line distance between A and B, let R be the magnitude of the particle displacement, and let S be the distance the particle traveled. A 33% Part (a) Which is always true? 33% Part (b) Which is only sometimes true? ▷ A 33% Part (c) Which can never be true? L=R O R>S R=S Grad Deduc Potent