Starting Point & Final Position Physics & Math Worksheet

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33. The cannon on a battleship can fire a shell a maximum distance of 32.0 km. (a) Calculate the initial velocity of the shell. (b) What maximum height does it reach? (At its highest, the shell is above 60% of the atmosphere—but air resistance is not really negligible as assumed to make this problem easier.) (c) The ocean is not flat, because the Earth is curved. 3 Assume that the radius of the Earth is 6.37x10 km . How many meters lower will its surface be 32.0 km from the ship along a horizontal line parallel to the surface at the ship? Does your answer imply that error introduced by the assumption of a flat Earth in projectle motion is significant here? 41. An owl is carrying a mouse to the chicks in its nest. Its position at that time is 4.00 m west and 12.0 m above the center of the 30.0 cm diameter nest. The owl is flying east at 3.50 m/s at an angle 30.0° below the horizontal when it accidentally drops the mouse. Is the owl lucky enough to have the mouse hit the nest? To answer this question, calculate the horizontal position of the mouse when it has fallen 12.0 m. vz sin 200 49. Derive R= for the range of a projectile on 8 level ground by finding the time t at which y becomes zero and substituting this value of t into the expression for x-xonoting that R = x - xo 50. Unreasonable Results (a) Find the maximum range of a super cannon that has a muzzle velocity of 4.0 km/s. (b) What is unreasonable about the range you found? (C) Is the premise unreasonable or is the available equation inapplicable? Explain your answer. (d) If such a muzzle velocity could be obtained, discuss the effects of air resistance, thinning air with altitude, and the curvature of the Earth on the range of the super cannon. 51. Construct You for the position at which the sandal hits the deck. 62. The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of 2.20 m/s in a direction 30.0° east of north relative to the Earth. It encounters a wind that has a velocity of 4.50 m/s in a direction of 50.0° south of west relative to the Earth. What is the velocity of the wind relative to the water?
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5

Suppose you first walk 12.0 m in a direction west of north and then 20.0 m in a
direction 40.0∘40.0∘ south of west. How far are you from your starting point, and what is the
compass direction of a line connecting your starting point to your final position? (If you
represent the two legs of the walk as vector displacements A and B , as in Figure 3.56, then this
problem finds their sum R = A + B.)
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.x=20 cos 40 =19.43m
Y=12 sin 20 =1.579
Rx =AX+BX =-(12 sin 20) –(20 cos40) =19.43m
Ry =√(Ay+Ry)2 =√-(19.43)2+-(-1.579)2
y=19.5m
angle= tan-1y/x
=4.650 South of west

10
Find the magnitudes of velocities vA and vB in the figure below, where,θ = 23.5° and vtot = 6.48 m/s

Apply sin rule
Va= 6.48 sin 23/6.48 sin(180-23-26.5)
Va= 3.33m/s
Vb =6.48 sin 26.5/6.48 sin(180-23-26.5)
Vb =3.80m/s

16

Solve the following question using analytical techniques.Suppose you walk 18.0 m
straight west and then 25.0 m straight north. How far are you from your starting point,
and what is the compass direction of a line connecting your starting point to your final
position? (If you represent the two legs of the walk as vector displacements...


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