While playing catch with your sister, you accidentally throw a tennis ball past her and horizontally out the window of your third floor apartment. If a window washer is startled by the passing tennis ball and drops her sponge from rest at that very moment, which describes the subsequent motion of the tennis ball and sponge? (you may ignore air resistance)
A. The tennis ball hits the ground first.
B. The tennis ball and sponge hit the ground at the same time.
C. The sponge hits the ground first.
D. None of the above.
Tamika is rearranging her furniture in preparation for having guests over. She exerts a constant force F to push her couch from one side of the living room at position s1 the other side of the living room at position s2. However, she decides it's not great to have the couch all the way on one side of the room, so she pushes it back away from wall a bit to position s3, again with force F. Which equa-tion describes the total work done by Tamika?
A. W = F (2s2 - s1 - s3)
B. W = F (s2 - s1 - s3)
C. W = F (s3 - s1)
D. W = F (s2 - s1)
W=f (s2- s1 -s3)
For the first question, we can analyze the motion of the tennis ball and sponge separately. Since both objects are dropped from rest, we can use the equations of motion to determine their subsequent motion.
The horizontal motion of the tennis ball is independent of its vertical motion. Since there is no horizontal force acting on the ball (ignore air resistance), it will continue moving horizontally at a constant velocity due to inertia. Therefore, the tennis ball will continue moving horizontally out the window at the same speed.
The sponge, on the other hand, experiences vertical motion due to gravity. When it is dropped from rest, it accelerates downwards due to the force of gravity. The acceleration due to gravity is constant, which means the vertical motion of the sponge follows the equations of motion for constant acceleration.
Knowing this, we can conclude that the tennis ball and sponge will hit the ground at different times. Since the tennis ball continues moving horizontally at a constant velocity, it will take longer to reach the ground compared to the vertically accelerating sponge. Therefore, the answer is:
C. The sponge hits the ground first.
For the second question, we need to determine the total work done by Tamika as she moves her couch. Work is defined as the product of force and displacement, and in this case, Tamika exerts a constant force F throughout the entire process.
To calculate the work done, we need to consider the different stages of motion. Tamika initially pushes the couch from position s1 to position s2 with force F, resulting in a displacement of (s2 - s1). The work done during this stage is given by the equation W1 = F * (s2 - s1).
Next, Tamika pushes the couch from position s2 back to position s3 with the same force F. This results in a displacement of (s3 - s2). The work done during this stage is given by the equation W2 = F * (s3 - s2).
To find the total work done, we add the work done in each stage:
W = W1 + W2
= F * (s2 - s1) + F * (s3 - s2)
= F * (s2 - s1 + s3 - s2)
= F * (s3 - s1)
Therefore, the equation that describes the total work done by Tamika is:
C. W = F * (s3 - s1)