SVDVD-103 JAV ormals on a surface to create a unit normal vector field that can be used to measure surface area and perform divergence in surface integrals. The unit normal function can be defined at any point on the surface by [vec N(t) = frac{frac{partial vec r}{partial t} imes frac{partial vec r}{partial t}}{||frac{partial vec r}{partial t} imes frac{partial vec r}{partial t}||}] The cross product of the two vectors is always perpendicular to both, making it a unit normal vector. The relationship between the cross product and the 4D is important here. [vec N(t) = frac{frac{partial vec r}{partial t} imes frac{partial vec r}{partial t}}{||vec}### Step 1: Understand the Problem The first step is to grasp what the problem is asking. The problem involves two bodies: one has a mass of ( m ), and the other has a mass of ( 3m ). Both bodies are thrown simultaneously, but with different initial heights and speeds. The task is to determine which of the two bodies will reach the ground first. ### Step 2: Analyze the Given Information From the problem, we can extract the following information: 1. The variables ( m ) and ( 3m ) represent the masses of the two bodies. 2. Both bodies are thrown simultaneously, meaning they start their motion at the same time. 3. The initial heights and speeds of the two bodies are different. Since the problem doesn't provide specific values for initial heights and speeds, we'll have to make some logical assumptions to proceed. ### Step 2: Make Logical Assumptions In order to solve the problem, I'll make the following assumptions: 1. The bodies are thrown vertically upwards, meaning their motion is along the vertical axis. 2. The problem involves the assumption that the only force acting on the bodies is gravity, meaning there's no air resistance or other forces. 3. The bodies' speeds remain constant throughout their motion (this is a simplification, but used for the sake of solving the problem). These assumptions will help simplify the problem and enable me to approach it systematically. ### Step 3: Determine the Outcome Given the two bodies, with masses ( m ) and ( 3m ), both are thrown simultaneously. The body with a mass of ( 3m ) has a greater mass than the one with a mass of ( m ). Since both bodies are thrown simultaneously, the difference in their masses will theoretically affect their motion. In classical physics, the mass of an object doesn't typically influence its rate of falling under gravity (assuming no other forces are present). Both bodies should reach the ground at the same time, assuming their initial heights and speeds are the same. However, the problem states that the two bodies have different initial heights and speeds. This means that despite their masses, whichever body is thrown with a higher speed or is released from a greater height will reach the ground sooner. Since the problem doesn't provide specific values for initial speeds and heights, I can't determine which of the two bodies will reach the ground first. Nonetheless, I can conclude that the body with either a higher initial speed or a greater initial height will reach the ground faster. ### Step 4: Finalize the Answer Given the limited information, I can't definitively determine which of the two bodies will reach the ground first. Nevertheless, I can conclude that a body with a higher initial speed or a greater initial height will have a shorter time to fall to the ground. Therefore, the body that will reach the ground first is the one that has a greater initial speed or is thrown from a greater height. **Final Answer:** The body with a higher initial speed or a greater initial height will reach the ground first. - Cuplikan Gratis dan Subtitle Bahasa Indonesia srt.

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