1. Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? If you represent the two legs of the walk as vectors A and B as in the figure below.
In this figure coordinate axes are shown. Vector A from the origin towards the negative of x axis is shown. From the head of the vector A another vector B is drawn towards the positive direction of y axis. The resultant R of these two vectors is shown as a vector from the tail of vector A to the head of vector B. This vector R is inclined at an angle theta with the negative x axis.
2. A 3.0 kg box is pulled by applying a force with magnitude 8.0 N at an angle of 60⁰ above the horizontal as shown below, what are the x and y components of the force, F.
3. What are the horizontal and vertical components of the net force on block A shown below.
4. What are the horizontal and vertical components of the net force on block B?
5. What forces need to be applied (magnitude and direction) to the block A for it to be stationary? What forces need to be applied to the block B.
6. Find the horizontal and vertical components of the acceleration if each block has a mass of 4.5 kg.
7. Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N to the left, the second a force of 90.0 N to the right, friction has a magnitude of 12.0 N, and the mass of the third child plus wagon is 23.0 kg.
a. Draw a free-body diagram, including all forces acting on the third child.
b. Calculate the child’s acceleration.
c. What would the acceleration be if friction were 15.0 N?
8. A 35.0-kg dolphin decelerates from 12.0m/s to 7.50 m/s in 2.30 s to join another dolphin in play. What is the deceleration of the dolphin? What average force was exerted to slow him if he was moving horizontally? (The weight of the dolphin is balanced by the upward buoyant force of the water.)
9. A box with mass 32.5 kg rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force of 14.0N to the box causing it to accelerate to the right.
a. What is the acceleration produced?
b. How far does the crate travel in 10.0 seconds?