In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.5 km 45° north of west; then 4.70 km 60° south of east; then 5.1 km straight east; then 7.2 km 55° south of west; and finally 2.8 km 10° north of east. What is his final position relative to the island? km ° south of east
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1.In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines:
2.5 km 45° north of west; then
4.70 km 60° south of east; then
5.1 km straight east; then
7.2 km 55° south of west; and finally
2.8 km 10° north of east.
What is his final position relative to the island?
km
° south of east
2.An archer shoots an arrow at a 74.0 m distant target, the bull's-eye of which is at same height as the release height of the arrow.
(a) At what angle must the arrow be released to hit the bull's-eye if its initial speed is 34.0 m/s? (Although neglected here, the atmosphere provides significant lift to real arrows.)
°
The cannon on a battleship can fire a shell a maximum distance of 36.0 km.
(a) Calculate the initial velocity of the shell.
m/s
(b) What maximum height does it reach? (At its highest, the shell is above a substantial part of the atmosphere--but air resistance is not really negligible as assumed to make this problem easier.)
m=?
(c) The ocean is not flat, since the earth is curved. How many meters lower will its surface be 36.0 km from the ship along a horizontal line parallel to the surface at the ship?
m. Does your answer imply that error introduced by the assumption of a flat earth in projectile motion is significant here? (Select all that apply.)
3.An owl is carrying a mouse to the chicks in its nest. It is 4.00 m west and 12.0 m above the center of the 30 cm diameter nest and is flying east at 3.50 m/s at an angle 34° below the horizontal when it accidentally drops the mouse. Will it fall into the nest? Find out by solving for the horizontal position of the mouse (measured from the point of release) when it has fallen the 12.0 m.
m (from the point of release)
3. Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.45 m/s, and the second a velocity of 4.25 m/s.
(a) What is the velocity of the second runner relative to the first?
m/s faster than the front runner.
(b) If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity?
The first runner will win.The second runner will win.
(c) What distance ahead will the winner be when she crosses the finish line?
m
A ship sets sail from Rotterdam, The Netherlands, heading
4. A knife is dropped from the top of a 10.0 m high mast on a ship moving at 1.75 m/s due south.
(a) Calculate the velocity of the knife relative to the ship when it hits the deck of the ship.
m/s (down)
(b) Calculate the velocity of the knife relative to a stationary observer on shore.
m/s ° (below the horizontal to the south)
(c) Discuss how the answers give a consistent result for the position at which the knife hits the deck.
5. What net external force is exerted on a 1350-kg artillery shell fired from a battleship if the shell is accelerated at 2.20 ✕ 104 m/s2? (Enter the magnitude.)
N
What is the magnitude of the force exerted on the ship by the artillery shell?
N
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