A submarine dives from the water surface at an angle of 30° below the horizontal, following a straight path 50 m long. How far is the submarine then below the water surface? (a) 50 m (b) (50 m)/sin 30° (c) (50 m) sin 30° (d) (50 m) cos 30° (e) none of those answers.

For the vectors a (a) Number as (b) a magnitude and (c) an angle (relative to î in the range of (-180°, 180°]). Now give bain (d) unit-vector notation, and as (e) a magnitude and (f) an angle (relative to î in the range of (-180°, 180°]) (b) Number (c) Number (d) Number = (3.0 m )î + (4.0 m )ĵ and 7 = (5.0 m )î + ( − )î + ( (f) Number i (e) Number i î + Units Units Î+ Units − 2.0 m )î,give a + b in (a) unit-vector notation, and Units ◄► ◄► Ĵ Units Ĵ Units

A pilot flies with a plane 20 km northward with an angle of 60 east ➚ , then 30 km to the east ⮕ , then 10 to the  north ⬆ , what is its distance from the start and what is its direction

Here are two vectors: [4.00m 4.00 m and b 6.00 m + (8.00 m What are |(f) the angle of a + ; (g) the magnitude and (h) the angle of D - a ; and (i) the magnitude and (j) the angle of a - b? (State your angle as a positive number.) (k) What is the angle between the directions of a - b ? and (a) Number 5.7 Units (b) Number Units ° (degrees) -45 (c) Number 10 Units (d) Number Units P (degrees) 53.13 (e) Number 10.77 Units (f) Number Units (degrees) 29.68314017

A hockey player faces the goal, which is 15.0 m in front of him (due north). Instead of trying to make a direct shot, the player passes the puck to a teammate who is 6.00 m away in a direction 30.0° to the right of the direction to the goal. What final displacement is needed to score a goal?

A snow-covered ski slope makes an angle of 0slone = 30.0° with the horizontal. When a ski jumper plummets onto the hill, a parcel of splashed snow is thrown up to a maximum displacement of 1.60 m at 0, = 18.0° from the vertical in the uphill snow direction as shown in the figure below. snow Oglope (a) Find the component of its maximum displacement parallel to the surface. m (b) Find the component of its maximum displacement perpendicular to the surface.

A secret agent skis off a slope inclined at θ = 31.5 degrees below horizontal at a speed of v0 = 14.7 m/s. He must clear a gorge, and the slope on the other side of the gorge is h = 18.4 m below the edge of the upper slope. What is the maximum width, w, of the gorge (in meters) so that the agent clears it?

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Consider the two vectors  = A= 5 î − ĵ and B = − î − 6 ĵ. (a) Calculate  A+B (b) Calculate  − A-B(c) Calculate |A+B|(d) Calculate|A-B|   (e) Calculate the directions of  A+B  and  A−B .   A+B = ? (counterclockwise from the x axis) A-B = ? (counterclockwise from the x axis)

A radar station sends a signal to a ship which is located a distance 13.0 kilometers from the station at bearing 136° clockwise from the north. At the same moment, a helicopter is at a horizontal range of 19.6 kilometers, at bearing 148° clockwise from the north, with an elevation of 2.59 kilometers. Let east be the ↑ direction, north be the ĵ direction, and up be the k direction. (a) What is the displacement vector (in km) from the helicopter to the ship? (Express your answer in vector form. Do not include units in your answer.) D = (b) What is the distance (in km) between the helicopter and ship? km (c) What If? The ship begins to sink at a rate of 5.50 m/s. Write the position vector (in km) of the ship relative to the helicopter as a function of time as the ship sinks. Assume that the helicopter remains hovering at its initial position and that the sinking rate remains the same even after the ship sinks under the surface. (Use the following as necessary: t. Do not include units in…