Write as a Vector Equality

Problem

x=240*cos(a)*t,2150=240*sin(a)*t−1/2*(9.8)*t2,3050=2150+x2

Solution

1. Identify the components of the position vector r*(t) from the given parametric equations for x and y

2. Define the horizontal component x(t) as the first element of the vector.

3. Define the vertical component y(t) as the second element of the vector, using the provided quadratic expression in t

4. Express the relationship between the variables as a single vector equation r*(t)=<x(t),y(t)>

5. Incorporate the magnitude constraint 3050=2150+x2 which implies the vector r reaches a specific point where its magnitude squared equals 3050

Final Answer

r*(t)=<240*cos(a)*t,240*sin(a)*t−4.9*t2>

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