# Physics: Velocity, Magnitude and Direction

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Hi, I need some assistance with the following questions:

1. A cannon ball is fired with a velocity of 48 m/s at 42 degrees up from the horizontal. Assume that it lands at the same level as it was fired from.

a. Find the maximum height of the cannon ball.

b. Find the total time the cannon ball is in the air.

c. Find the range of the cannon ball.

2. A rock is thrown off a vertical cliff with a horizontal velocity of 15 m/s. If the rock lands 25 m from the base of the cliff, how tall is the cliff?

(A) 8 m (B) 14 m (C) 16 m (D) 34 m

3. Velocity A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in length and points along the negative y-axis. Use graphical methods to find the magnitude and direction of the vectors(a) A + B and (b) A - B.

4. A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0 degrees above the horizontal. Next, it travels 135 ft at an angle of 40 degrees below the horizontal. Use graphical techniques to find the roller coaster's displacement from its starting point to the end of this movement.

5. A jogger runs 100 m due west, then changes direction for the second leg of the run. At the end of the run, she is 175 miles away from the starting point at an angle of 15.0 degrees north of west. What were the direction and length of her second displacement? Use graphical techniques.

6. The magnitude of vector A is 35.0 units and points in the direction 325 degrees counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector.

7. A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

8. A brick is thrown upward from the top of a building at angle of 25 degrees to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building?

9. A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0 degrees above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectile's velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?

10. A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.0 m/s aimed directly north relative to the water.

(a) What is the velocity of the boat relative to the shore.

(b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north

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