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Exam 3: Motion in Two Dimensions

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Question 1

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A 0.20-km wide river has a uniform flow speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. In what direction must the boat be pointed in order to accomplish this?

A) 23 $\degree$ west of north
B) 20 $\degree$ west of north
C) 24 $\degree$ west of north
D) 22 $\degree$ west of north
E) 17 $\degree$ west of north

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Question 2

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A racing car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car?

A) 8.8 m/s2
B) 7.5 m/s2
C) 9.4 m/s2
D) 6.3 m/s2
E) 5.3 m/s2

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Question 3

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A stunt pilot performs a circular dive of radius 800 m. At the bottom of the dive (point B in the figure) the pilot has a speed of 200 m/s which at that instant is increasing at a rate of 20 m/s2. What acceleration does the pilot have at point B?

A projectile starts at the coordinate origin, where the displacement vector also originates. The initial velocity, v0, makes an angle $\theta$ 0 with the horizontal where 0 < $\theta$ 0 < 90 $\degree$ . At the instant when the projectile is at the highest point of its trajectory, the displacement, velocity and acceleration vectors are $\overrightarrow{\mathbf{r}}$ , $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{a}}$ . Which statement is true?

Raindrops are falling straight downward. When observed from a car travelling at 55.0 mi/h, the drops streak the side window at an angle of 60.0 $\degree$ with the vertical. Find the speed with which the drops are falling.

A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. What is the speed of the boat relative to the water?

A block is supported on a compressed spring, which projects the block straight up in the air at velocity $\overrightarrow{\mathbf{v}}=v_{0y} \hat{\mathbf{j}}$ . The spring and ledge it sits on then retract. You can win a prize by hitting the block with a ball. When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the block reaches the ground and that the ball is thrown from a height equal to the release position of the block.)

A car travels in a due northerly direction at a speed of 55 km/h. The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal. If the rain is falling vertically with respect to the earth, what is the speed of the rain with respect to the earth?

Two vectors starting at the same origin have equal and opposite x components. Is it possible for the two vectors to be perpendicular to each other? Justify your answer.

At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i - 4.0j) m/s2. At the instant the x coordinate of the particle is 15 m, what is the speed of the particle?

A Ferris wheel at Luna Park has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride?

The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east. If his speed relative to the ground is 80 km/h, what is the speed of his airplane relative to the air?

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What is the magnitude of the average velocity for this trip?

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by: $\overrightarrow{\mathbf{r}}=\left(1.61 \times 10^{6} \tilde{\mathbf{i}}+3.00 \times 10^{3} \hat{\mathbf{j}}\right) \mathrm{m}$ and $\overrightarrow{\mathbf{v}}=(150 \hat{\mathbf{i}}+21 \hat{\mathbf{j}}) \frac{\mathrm{m}}{\mathrm{~s}}$ .The plane is most likely:

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west, and the acceleration of the car has components of 2.4 m/s2 east and 1.8 m/s2 south. What is the radius of the circle?

Imagine that you are going for a ride in a hot air balloon at the Canowindra Balloon Challenge. While the balloon is rising at a speed of 2.0 m/s, you throw a small ball down at a speed of 5.0 m/s relative to your body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is

A Olympic athlete in the long jump goes into the jump at 12 m/s and launches himself at 20 $\degree$ above the horizontal. How long is he in the air before returning to Earth?

A cricket ball is hit at ground level. The ball is observed to reach its maximum height above ground level 3.0 s after being hit. And 2.5 s after reaching this maximum height, the ball is observed to barely clear a fence that is 97.5 m from where it was hit. How high is the fence?

An explorer wishes to cross a river that is 1.5 km wide and flows with a velocity of 5.0 km/h parallel to its banks. The explorer uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time for crossing?

A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0 $\hat{\mathbf{i}}$ - 2.0 $\hat{\mathbf{j}}$ ) m/s2. At the instant the particle moves back across the x axis (y = 0) , what is the value of its x coordinate?