A car drives on a curved road that goes down a hill. The car's position is defined by the position vector, r = { [30.0 cos (t)] + [30.0 sin(t)] j — (A₂t)k} ftwhere A₂ = 19.0ft/s. The image below shows the system projected onto the x-y plane. What are the car's velocity and acceleration vectors at this position? Draw your vectors starting at the black dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded and the trigonometric function arguments are in radians. ► View Available Hint(s) I No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. -30 ft-

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Show, using graphical vector addition, that the acceleration vector for an object in uniform circular motion points toward the center of the circular path. Use the factthat acceleration in two or more dimensions is defined as

A projectile is shot from a top of a building 96 feet high from a gun at an angle of 30 degrees with the horizontal. If the muzzle speed is 1600 ft/sec, a. Find the position vector of the shot.

An object is moving in a circle of radius 10 cm centered on the origin in the xy-plane at a constant speed of 5 m/s.

A swimmer tries to cross a river swimming at the angle θ to theperpendicular to the stream (to the left). The speed of the swimmer isv’, the speed of the river u (to the right) is unknown, and the width ofthe river is h. The swimmer lands at the distance ? to the right fromthe opposite point at the other side of the river. What was the speed ofthe river?

A clif with an angled summit 900 m above the valley foor is a popular jumping of point for base jumpers.One particular base jumper gets a running start and runs of the side of the clif with a velocity of 4.00 m/sat an angle that is 25.0◦ below the horizontal, as shown.(a) How long is the base jumper in the air before she opens her parachute 150 m above the valley foor?(b) How far (horizontally) is she away from the clif?

5. Review. A snowmobile is originally at the point with posi- tion vector 29.0 m at 95.0° counterclockwise from the x axis, moving with velocity 4.50 m/s at 40.0°. It moves with constant acceleration 1.90 m/s² at 200°. After 5.00 s have elapsed, find (a) its velocity and (b) its position vector.

The velocity and acceleration vectors of a moving object are always perpendicular. O True O False

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