Question

These problems maybe from Newton's Law, Motion, Vector, and Work and Energy, make sure to use the correct formula.  Round four decimal places throughout the entire problem and for the final answer for each problem.

1. A velocity vector 15 m/s has an angle 30 degree with x axis and another velocity vector 40 m/s, has an angle 90 degree with x axis. What is the angle of the resultant with reference first vector?

Instruction - Take sine of your result

2. A krypton atom (mass 83.9 u) moving with a velocity of 0.75 km/s to the left and a water molecule (mass 18.0 u) moving with a velocity of 0.39 km/s to the right collide head-on. The water molecule has a velocity of 0.636 km/s to the left after the collision. What is the velocity of the krypton atom after the collision? [use negative sign for left and positive sign for right direction]

3.Two blocks of masses m1 =2 kg and m2 = 2 kg are connected by a string. One block (m1) slides on a table and the other (m2) hangs from the string, which passes over a pulley. The coefficient of kinetic friction is 0.20. What is acceleration of the blocks?

4.A car in rest started moving with acceleration 4.0 m/s^2. After 5.8 sec, the driver saw a deer on the road and applied brake and came to a complete stop after traveling TOTAL distance of 273 meter from the starting point. What was the Deceleration rate (a) after brake was applied?

Answer 1

1)

and

The resultant makes an angle with the first vector. and is the angle between the two vectors and .

Then

Resultant vector makes an angle with the first vector.

2)

Conserving the momentum of the krypton atom and water molecule before and after collision,

Velocity of krypton atom after collision is

3)

Net force acting on the first block( on the table) in the direction of motion is

( T is the tension in the string)

Net force acting on the second block (hanging) in the direction of motion is

From above equations, Acceleration of the blocks is

4)

Distance travelled by car before brakes were applied,

Speed of the car at the time when brakes were applied,

Total distance travelled by car from starting point

Distance travelled by car after the brakes were applied,

Using

Deceleration of car after the brake was applied is