# Tutor profile: Hannah W.

## Questions

### Subject: Trigonometry

Kelly is trying to retrieve a frisbee on her roof that begins 10 feet above the ground. She has 13 foot ladder that will help climb to the top. At what angle above the horizontal must she place the ladder so that the top of ladder meets exactly with where the roof begins 10 feet above the ground?

Given the law of sines and cosines commonly referred to as SOHCAHTOA, we can set up an equation that will allow us to find the angle above the horizontal or the angle between the ground and the ladder. Because we have the length opposite the angle (10 feet) in question and the hypotenuse (13 feet) we can set up the equation $$ sin\theta = 10/13 $$. We must then find $$ \theta $$ by taking the inverse sin (in order solve for a variable inside of a function we must apply the inverse function, just like if we needed a variable that was being multiplied by a number, we must divide by that number in order to solve for said variable.) It would look like this: $$ sin \theta = 10/13$\\ $$ sin\theta = .7692$\\ $$\sin^{ - 1} (sin\theta)=sin^{ - 1}(.7692)$\\ $$\theta = 50.3^{\circ}$$

### Subject: Algebra

Create an algebraic equation to answer the following question. Jolene is selling her apples for $3.00 a pound. While Janice is selling her apples for $2.00 a pound with an initial fee of $2.00. After how many apples will the total price for Jolene and Janice's apples be the same?

If we choose to denote P as the total price and a as the number of apples, Jolene's apples will cost $$ P = 3a $$ and Janice's apples will cost $$ P = 2 + 2a $$. Given that we want to know the how many apples will cause both girls to have the same total price, we must set the equations equal to one another ( P = P ). After doing so we get $$ 3a = 2 + 2a $$ and then we must solve for a (the number of apples). We will then solve for a as such: $$ 3a = 2 + 2a $\\ $$ 3a - 2a = 2 + 2a - 2a $$ and we are left with a = 2\\ or 2 apples.

### Subject: Physics

A 75 kg man slips off of the edge of a 3 story building. If the maximum amount of impact speed the human body can survive is about 14 m/s, ignoring air resistance, does the man survive the fall? (Each story is 3 meters)

Given that we are ignoring air resistance, mass is negligible for objects in free-fall motion. We can use basic kinematics to solve this problem. Given that $$ \triangle v^2 = -2a\triangle y $$ with the acceleration due to gravity being -9.8 m/s and the fall height 9 meters (3 stories multiplied by 3 meters) we can substitute in to get $$ \triangle v^2 = -2(-9.8)(9) $$. After some simplifying, we find that $$ \triangle \sqrt v^2 =\sqrt(-2(-9.8)(9)) $$ or $$ \triangle v =13.28 m/s $$. He survived!!

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