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# Vectors - Force & Velocity

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1) A truck is stuck in the mud. One winch can pull on a cable with 2500 pounds of force and a second winch can pull with 1500 pounds of force. If the angle between the cables is 25 degrees, what is the result force on the truck? Show method used.

Cable 1: 2500 pounds
Theta=25 degrees

Cable 2: 1500 pounds

2) During the rodeo, a clown runs 9.3m north, turns 29 degrees east of north, and runs 1.1m. Then after waiting for the bull to come near, the clown turns due east and runs 6.6m to exit the arena.

a) What is the magnitude of the clowns total displacement? The answer I received was 12.5m which was correct, but the second part was wrong.

b) How many degrees east of north is the clowns total displacement? Answer in degrees. I was given 55.2 degrees. This answer is wrong.

3) The pilot of an aircraft wishes to fly due west in a 51.3km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 206km/h.

a) How many degrees from west should the aircraft head? Let clockwise be positive. Answer in degrees. Given 13.98 degrees - wrong.
b) What should the planes speed be relative to the ground? Answer in km/h.

4) A particle undergoes 2 displacements. The first has a magnitude of 163cm and makes an angle of 101.7 degrees with the positive x axis. The resultant displacement of the 2 displacements is 97cm directed at an angel of 25.4 degrees to the positive x axis. Find the magnitude of the second displacement. Answer in units of cm.
a) Find the angle of the second displacement, measured from the positive axis, with counterclockwise positive within the limits of -180 degrees to +180 degrees. Answer I degrees.

***** Now, got answer of 168.78 cm and was right, but part a was wrong with an answer of 135.64 degrees.

5) Two airplanes leave an airport at the same time. The velocity of the first airplane is 740m/h at a heading of 22.5 degrees. The velocity of the second is 640m/h at a heading of 120 degrees. How far apart are they after 1.9 hours? Answer in units of meters.

6) An auto graphed baseball rolls off a 1.1m high desk and strikes the floor 0.70 m away from the desk. The acceleration of gravity is 9.81m/s^2. How fast was it rolling off the desk before it fell off? Answer in m/s. Wrong answer is 1.85 meters.

7) An electron beam in a tv moves with a horizontal velocity of 4.4*10^7m/s across the crt and hits the screen, 46cm away. G = 9.8m/s^2. How far does the electron beam fall while traversing the distance? Answer in meters. Wrong answer is 4.905*10^-16

8) A rock is projected from the edge of the top of a building with an initial velocity of 14m/s to an angle of 30.2 degrees above the horizontal. Due to gravity, the rock strikes the ground at a horizontal distance of 37.4m from the base of the building. Assume the ground is level and that the side of the building is vertical. The acceleration of gravity is 9.8m/s^2. How tall is the building? Answer in meters. Wrong answer is 46.83.

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#### Solution Preview

Please see the attached file.

1) A truck is stuck in the mud. One winch can pull on a cable with 2500 pounds of force and a second winch can pull with 1500 pounds of force. If the angle between the cables is 25 degrees, what is the result force on the truck? Show method used.

Cable 1: 2500 pounds
Theta=25 degrees

Cable 2: 1500 pounds

Considering the typical X-Y plane,
Let F1 be the force of Cable 1 and F2 be the force of cable 2.
X-Component of F2 = 1500*Cos 25 = 1360 lb
Y-Component of F2 = 1500*Sin 25 = 644 lb
X-Component of F1 = 2500 lb
Y-Component of F1 = 0

X-Component of resultant = 1360+2500 = 3860 lb
Y-Component of the resultant = 644 lb

Result Force = sqrt(3860^2 + 644^2) = 3913.4 lb at an angle of,
Arctan(644/3860) = 9.5 degrees clockwise from F1.

Or, 3913.4 @ -9.5 deg, assuming that the angle is measured from the x-axis in a counterclockwise.

2) During the rodeo, a clown runs 9.3m north, turns 29 degrees east of north, and runs 1.1m. Then after waiting for the bull to come near, the clown turns due east and runs 6.6m to exit the arena.

a) What is the magnitude of the clown's total displacement? The answer I received was 12.5m which was correct, but the second part was wrong.

b) How many degrees east of north is the clown's total displacement? Answer in degrees. I was given 55.2 degrees. This answer is wrong.

Total X-Component of displacement = 1.1Cos 29 + 6.6 = 7.56 m
Total ...

#### Solution Summary

The velocity and force are provided with explanation in an attachment.

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