Tutor profile: Thomas L.
Subject: Physics (Newtonian Mechanics)
A 5 cubic centimeter aluminum ball is dropped from a 100 meter high building. What is the momentum of the ball at the base of the building.
Although this question is short, there are multiple portions. To determine the momentum, we will need to determine the mass and velocity of the ball the instance it contacts the base. Since the volume and material of the ball was provided, we can determine the mass from the density of aluminum (2.7 g/cm^3). By multiplying the volume with the density, we obtain a mass of 13.5 grams. As there are no other external forces acting on the ball besides gravity, we can assume a initial velocity of zero m/s and use newtonian kinematics to determine the final velocity. The final velocity is equal to the initial velocity plus the velocity acquired by acceleration in the travel time. Thus we will also need to the time the ball took to travel the length of the building. From the kinematic equation, change in x = initial velocity*time + 1/2 acceleration*time^2, we see that time is = sqrt(2*change in x / acceleration). This give us a travel time of ~4.5 seconds, which in tern gives a final velocity of 44.1 m/s. With the mass and the final velocity, we can determine a momentum of 595.35 g*m/s
A circle or radius r is inscribed in a square. What is the area of the top left corner of the square?
While it may seem there is not enough information, this problem is still achievable. You need to recognize that the length of the square's side is 2r since the circle is inscribed. Moving on to solving the problem, we can now determine the area of the square (side^2) and the area of the circle (pi*radius^2). By taking the area of the circle (pi*r^2) from the area of the square (4r^2), the remainder is the area of the 4 corners ([4-pi]r^2). Since each corner are identical in area, we can take the remainder and divide it into fourths and determine the area of one of the corner.
Solve for x in the following equation: 9x + 2 = 7x - 4.
While this may seem challenging with x's on both sides, it is quite straightforward. First, subtract 7x from both sides to move x to one side of the equations. 2x + 2 = -4. Next, we will clean up the left-hand side by subtracting 2 from both sides. 2x = -6. Now it is a simple division of 2 from both sides to isolate x. x = -3.
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