A hunter aims directly at a target (on the same level) 38.0 m ...

Question

A hunter aims directly at a target (on the same level) 38.0 m away.

(b) At what angle should the bow be aimed so the target will be hit?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A golfer hits a golf ball with an initial velocity of 40 m per second, aiming directly at a flag stick, positioned 150 m away on the same level of the course at what angle should the golfer aim their shot to ensure it reaches the flag stick. So that's our end goals. We're trying to figure out at what angle the golfer should aim in order to ensure that it reaches the flagstick. And that will be our final answer that we're ultimately trying to solve. For. Awesome. We're also given some multiple choice answers and they're all in units of degrees. So let's read them off to see what our final answer might be. A is 12, B is 23 C is 33 and D is 67. Awesome. So first off, let us note that the golfer or I should say the golf ball and the golfer in the flights flag stick are all located at the same level as stated in the prom itself. Therefore, we can recall and apply the level horizontal range equation which states that R is equal to V zero squared multiplied by sine of two multiplied by theta zero, all divided by G where R is the range. So let's make a little side note here that R is the range and it's equal to 150 m as given to us in the prom itself, V zero is equal to the initial velocity which is given to us as 40 m per second. And we're also, we should know right away that G denotes the acceleration due to gravity. And the numerical value for that is 9.8 m per second squared. And then finally, theta zero is the value that we're trying to solve for. We do not know what it is. That is the angle at which the golfer should aim in order to ensure that it's that they shot when they strike the golf ball will reach the flag stick. That's what theta zero represents. And that's the value that we do not know that we're trying to solve for. That's our final answer. Awesome. So now at this stage, we can plug in all of our known variables into our level horizontal range equation. And then we are gonna have to rearrange that equation to isolate and sulfur theta zero to find our final answer. So let's start to do that. So we know that R equals 150 m, which is equal to 40 m per second square is, that's our initial velocity multiplied by sine of two multiplied by theta zero all divided by our value for gravity which is 9.8 m per second squared. So we're gonna have to rearrange this equation. So to get started, let's try to get sine of two multiplied by theta zero onto one side. And when we do that, we'll get that sign of two multiplied by theta zero is equal to 150 m multiplied by gravity. So 9.8 m per second squared, all divided by our initial velocity squared. So 40 m per second squared. So our final step is we're gonna have to take inverse sign in order to get rid of the sign that's on the left. And then we're also gonna have to divide by two to finally get theta zero all by itself. So when everything's all set and done and getting theta zero by itself, it should be something that looks along the lines of this. So sign of so inverse sign, so inverse sign of 150 m multiplied by gravity which is 9.8 m per second squared, all divided by our initial velocity, which is 40 m per second squared. And this is all divided by two. So when we plug that into our calculator, and we round to the nearest hole number we will get to 33 degrees and this is our final answer. Hooray, we did it. So looking at our multiple choice answers, this corresponds with multiple choice answer letter C 33 degrees. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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A hunter aims directly at a target (on the same level) 38.0 m away.
(b) At what angle should the bow be aimed so the target will be hit?

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