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Hi! For today’s video, we’re going to solve a situational problem from the concept of projectile motion using Inverse Trig Function. The problem is: If an object is directed at an angle theta (with theta element of closed interval - 0 to pi over 2), then the range will be R is equals to v sub 0 squared over g times sine 2 theta (in feet) where v sub 0 (in feet per second) is the initial speed and g is equals to 32 feet per second squared is the acceleration due to gravity. At what angle shall the object be directed so that the range will be 100 feet, given that the initial speed is v sub zero is equals to 80 feet per second? The given are as follows: R is equals to 100 feet, where R represents the range. V sub 0 is equals to 80 feet per second, where it represents the initial speed and g is equals to 32 feet per second squared, which is the acceleration due to gravity.
To solve for this problem, let us plug in the given values to the formula provided to find the angle. The formula is R is equals to v sub 0 squared over g times sine 2 theta; substitute 100 to R, 80 squared to v sub 0 squared, 32 to g. It will be 100 is equals to 80 squared over 32 times sine 2 theta. Multiply both sides by 32 over 80 squared. Now let us reduce the 80 squared on the right side of the equation, and then reduce the numbers with the GCF 32. It would be 32 over 80 squared times 100 is equals to sine 2 theta, cancelling the term on the right side. For the left side of the equation multiply 32 over 80 squared with 100, or 100 over 1 in fraction. The product will be 3 200 over 80 squared. Evaluate the power, it will be 3 200 over
6 400. Reduce the fraction with 3 200, the product shall be one half is equals to sine 2 theta. The final step is to swap the sides of the equation: sine 2 theta is equals to one half. But we are not yet done. What we have accomplished is simply the value of sine 2 theta, but not the angle, which is represented by theta. To solve for the remaining problem, we should use the inverse function of sine. Two theta is equals to inverse sine of one half. Calculate, two theta is equals to pi over six. Divide it by two, the answer will be theta is equals to pi over 12 or 15 degrees. So the answer will be: "The object shall be directed at an angle of 15 degrees."
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