. You are working as an expert witness for the defense of a container ship captain whose ship ran into a reef surrounding an island. The captain is being charged with intentionally running the ship into the reef. In discovery, the following information is correct: The ship was traveling at 2.5 m/s toward the reef when a mechanical failure caused the rudder to jam in the straight-ahead position. At that point in time, the ship was 900 m from the reef. The wind was blowing directly toward the reef and exerting a constant force of 9.00 x 10³ N on the boat in a direction toward the reef. The mass of the ship and its cargo was 5.50 x 107 kg. During the preparation for the trial, the captain claims that without control of the direction of travel, the only choice he had was to put the engines in reverse at maximum power, such that the total force exerted by the frictional drag force of the water on the propeller was 1.25 x 105 N in a direction away from the reef. From this information, construct a convincing argument that nothing the captain could do in this situation could have prevented the ship from striking the reef.

In a naval battle, a cruiser is attempting to fire on a frigate. The cruiser is a distance d₁ = 2,050 m to the east of the peak of a mountain on an island, as shown in the figure below. The frigate is attempting to evade cannon shells fired from the cruiser by hiding on the west side of the island. The initial speed of the shells that the cruiser fires is v₁ = 245 m/s. The peak of the mountain is h = 1,690 m above sea level, and the western shore of the island is a horizontal distance d₂ = 270 m from the peak. What are the distances (in m), as measured from the western shore of the island, at which the frigate will be safe from fire from the cruiser? (Note the figure is not to scale. You may assume that the height and width of the frigate are small compared to d₁ and h.) less than Need Help? Read It 0₁ Ja₂ m, or more than d₁ m

A ball rolls off the edge of a table. Let the time the ball leaves the table surface be t = 0. If the table is horizontal, its velocity as a function of time is given by ✓ = 1.10î - 9.80tĵ, with v in m/s and t in s. The ball's displacement from the edge of the table from t = 0 to t = 0.395 s (while it is in flight), is given by Ar = Jo Ar = 0.395 Use this theorem to perform the integration: v dt. [ [ P + Qf(x)] dx = p[ dx + Q f f(x) dx. P[ Consider the units and unit vectors to be the constants P and Q. Integrate to determine the ball's displacement (in m) from the table edge at 0.395 s. (Express your answer in vector form. Do not include units in your answer.) m

A bicycle travels 7.50 km due east in 0.210 h, then 8.80 km at 15.0° east of north in 0.770 h, and finally another 7.50 km due east in 0.210 h to reach its destination. The time lost in turning is negligible. Assume that east is in the +x-direction and north is in the +y-direction. What is the direction of the average velocity for the entire trip? Enter the answer as an angle in degrees north of east

You throw a ball on planet X where g is not the same as on Earth. The figure below shows the vertical velocity of the ball after it leaves your hand. Air resistance is not important. v(m/s) 18.0 12.0 6.0 -6.0 -12.0 -18.0 1.0 2.0 3.0 t(s)

A river that is one-quarter of a mile wide is flowing at a speed of 1 mile per hour. A swimmer enters the river and swims directly toward the opposite bank at a speed of 6 miles per hour. The current alters the swimmer's direction and causes her to reach the opposite bank some distance downstream. Find the angle the swimmer's resultant path makes with the line directly across the river. (Use decimal notation. Give your answer to two decimal places. Include the degree sign in your answer.) angle How far downstream does the swimmer make landfall? (Give an exact answer. Use symbolic notation and fractions where needed.) distance = miles

A baseball with mass of 0.14 kg is batted into the air. Its initial speed is 47.4 m/s, directed at an angle 14 degrees above the horizontal. After 1.5 seconds, what is the vertical component of the ball's velocity (in m/s)? Use positive values for the upward direction, and negative values for the downward direction.