A jet airliner, moving initially at 250 mi/h to the east, suddenly enters a regi

Question

A jet airliner, moving initially at 250 mi/h to the east, suddenly enters a region where the wind is blowing at 90 mi/h toward the direction 30.0° north of east. What is the new speed and direction of the aircraft relative to the ground?
Answer: mph
Answer: °

north of east?

south of west?

north of west?

south of east?

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 16.6t and y = 4.04t 4.90t2, where x and y are in meters and t is in seconds.

By taking derivatives, do the following. (Give the answers in terms of t.)

An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 14.0 m if her initial speed is 4.00 m/s. What is the free-fall acceleration on the planet? (Ignore air resistance.)
Answer: m/s2

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.20 m. The mug slides off the counter and strikes the floor 1.80 m from the base of the counter.

(a) With what velocity did the mug leave the counter?
Answer: m/s

(b) What was the direction of the mug's velocity just before it hit the floor?
Answer: ° (below the horizontal)

To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 310 m/s at 51.0° above the horizontal. It explodes on the mountainside 39.0s after firing. What are the x and y coordinates of the shell where it explodes, relative to its firing point?
x = m
y = m

A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.40 m/s at an angle of 15.0° below the horizontal. It strikes the ground 6.00 s later.

(a) How far horizontally from the base of the building does the ball strike the ground?
Answer: m

(b) Find the height from which the ball was thrown.
Answer: m

(c) How long does it take the ball to reach a point 10.0 m below the level of launching?
Answer: s

Explanation / Answer

A = -4i -3j
B = 2i - 5j
C = -9i + 5j

a)
D = a + b +c
= -4i -3j + 2i - 5j -9i + 5j
= (-11 i -3 j) m

magnitude = sqrt (11^2 + 3^2) = 11.4 m
direction = 180 + atan (3/11)
= 195 degree

b)
D = - a - b + c
= 4i + 3j - 2i + 5j -9i + 5j
= (-7 i + 13 j) m

magnitude = sqrt (7^2 + 13^2) = 14.8 m
direction = 90 + atan (7/13)
= 118 degree

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