Vector A has x and y components of 5.46 cm and -3.86 cm, respectively; vector B has x and y components of 4.04 cm and -7.94 cm, respectively. If A - B + 2C = 0, the magnitude of C in centimeters is:

The height of a helicopter above the ground is given by h = 3.00 t3, where h is in meters and t is in seconds. After 1.93 s, the helicopter pilot lets go of a small mailbag. How long (in seconds) after its released does the mailbag reach the ground?

A particle moves along the x-axis. Its position is given by the equation x = 3 +7t - 6t2 with x in meters and t in seconds. Determine its velocity (in m/s) when it returns to the position it had at t = 0.

A motorist drives along a stright road at a constant speed of 31.6 m/s. Just as she passes a parked motorcycle police officer starts to accelerate at 2.92 m/s2 to overtake her. Assuming the officer maintains this acceleration, the time it takes (in seconds) the police officer to reach the motorist is:

The position of a particle can be described by r(t)=1.96i + 3.4t2j + 5.17 t3k . Where r(t) is in meters and t is in seconds. Determine the speed of the particle (in m/s) at t = 2.35 s is:

A test rocket is fired vertically upward from a well. A catapult gives it an initial velocity of 69.6 m/s at ground level. Its engines then fire and give it an upward acceleration of 5.34 m/s2 until it reaches an altitude of 1,084 m. At that point its engines fail and the rocket goes into free-fall with an acceleration of -9.80 m/s2. What is its maximum altitude (in kilometers) from ground.

A soccer player kicks a rock horizontally off a 40.4 m high cliff into a pool of water. If the player hears the sound of the splash 3.55 s later, what was the initial speed (in m/s) given to the rock? Assume the speed of sound in air to be 343 m/s.

A particle initially located at the origin has an acceleration of a = 2.82 j m/s2 and an initial velocity of vi = 5.75 i m/s. The speed of the particle (in m/s) at t = 4.92 s is:

A cannon with a muzzle speed of 906 m/s is used to start an avalanche on a mountain slope. The target is 2,748 m from the cannon horizontally and 849 m above the cannon. At what angle (in degrees and three significant figures), above the horizontal, should the cannon be fired? Use the approximation sinΘ≈Θ and cosΘ≈1. Multiply your answer by 57.3 to convert it to degrees.