16. The wheel of a bicycle has a radius of 40 cm. Calculate its period of revolution if the bicycle moves With a speed of 20 km/h. How much is the angular velocity?
17. Very large magnitude of acceleration can be achieved in some devices such as in a gun. A bullet in a gun is accelerated from the ring chamber to the end of the barrel at an average rate of 6.20*10³ m/s² for 8.10x10⁴ sec.
What is its muzzle velocity (that is, its final velocity?)
18. A 0.525 kg ball is attached to a 125 in string and swings in a circular path The angle of the string away from vertical is 30.0°. Find the centripetal force acting on the ball and the speed of the ball.
19. A car travels 20 km due north and then 25 km in a direction 60° West of North. Use both graphical and algebraic methods to find the magnitude and direction of a single vector that gives the net effect of the car's trip
20. A sailor boards a paddle boat and heads the boat Westward directly across a river. The river flows South at 50 cm/s and the woman paddles the boat with a speed of 100 cm/s.
A. Determine the resultant velocity of the boat-both magnitude and direction,
B. How far down stream relative to the straight-across direction will woman be when she reaches the opposite shore?
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1. The dot product of A and B can be defined alternatively as the magnitude of multiplied by the component B of in the direction of A. Find the angle between each of the following pairs of vectors.
a) 3i- j and i-2j
b) 3i-2j and i2j
(c) 3i -2jand 4i+ 6j
22. A driver of a vehicle traveling at a. speed of 30 m/s on a motorway brake sharply to a standstill in a distance of 100m. Calculate the deceleration of the vehicle.
23. A car driver accelerates her car by1.4 m/s, starting from rest.
(a) How long does it take her to reach a speed 1 of 2.0 m/s?
(b) If she then brakes to a stop in 0.8 seconds, what is her deceleration?
Only formulas no need of explanation!!
24. What is (a) the tangential velocity? (b) the angular velocity? and (c) the centripetal acceleration, du
to the Earth's rotation, of a body on the equator? Radius of Earth 6,400 km.
25. Determine a velocity vector that has a magnitude of 5 m/s directed along the direction of vector D= 1.5i+2j
16. Period of revolution (T) = (2πR) / v
where R is the radius of the wheel and v is the speed of the bicycle.
T = (2π * 40 cm) / (20 km/h * 100 cm/m)
17. Final velocity (v) = Initial velocity (u) + (acceleration * time)
v = 0 + (6.20 * 10^3 m/s^2 * 8.10 * 10^4 sec)
18. Centripetal force (F) = (mass * velocity^2) / radius
Speed (v) = radius * angular velocity
19. For graphical method, you can draw a vector diagram representing the car's displacement and find the magnitude and direction of the resultant vector.
For algebraic method, you can use vector addition and trigonometry to find the magnitude and direction of the resultant vector.
20. A. Resultant velocity magnitude = √((river velocity)^2 + (boat velocity)^2)
Resultant velocity direction = tan^(-1)((river velocity) / (boat velocity))
B. Distance downstream = (river velocity) * (time to cross the river)
21. No question provided.
22. Deceleration (a) = (final velocity^2 - initial velocity^2) / (2 * distance)
Distance = 100 m
23. a) Time taken (t) = (final velocity - initial velocity) / acceleration
b) Deceleration (a) = (final velocity - initial velocity) / time
24. a) Tangential velocity = 2πR / (24 hours) where R is the radius of the Earth
b) Angular velocity = 2π / (24 hours)
c) Centripetal acceleration = (angular velocity)^2 * R
25. Velocity vector = magnitude * direction
Direction can be found by calculating the unit vector of vector D.