A student solving a physics problem for the range of a...

A student solving a physics problem for the range of a projectile has obtained the expression R= v20sin(2\theta )g where v0=37.2meter/second , \theta =14.1∘ , and g=9.80meter/second2 . Use your calculator to evaluate R . View Available Hint(s) for Part C Hint 1 for Part C. Inserting values into the equation Write down the expression with the given values and units replacing the variables. Hint 2 for Part C. Verify proper use of the calculator Make sure you verify how your calculator performs the necessary operations using it to calculate expressions for which you know the answer. Hint 3 for Part C. One-step-at-a-time Use the one-step-at-a-time strategy, where one step will be to multiply \theta by 2 before you evaluate the sine function. 66.7meter 69.5meter 31.5meter 10.5meter

Transcript

00:01 So we are given two different equations here, right? we have r equals v squared sine times 2 divided by that g.

00:16 And then the second equation we're given is t equals 2 v sine divided by g.

00:29 Now it wants us to rearrange the equation, right, in terms of all right? r, v, and t.

00:36 Okay, so we need to get rid of this variable.

00:39 We need to get rid of g, right? because that's not anywhere in our answer.

00:43 So we could use the substitution method to help us get rid of g.

00:47 So i just need to rearrange this equation.

00:50 All right.

00:51 What we could do to rearrange that equation is just isolate g, which would mean multiplying both sides by g and then dividing both sides by t.

00:59 And you end up with g equals 2b sign, the angle divided by t right so these two equations are saying the same thing one is just solving for g and one is solved in terms of t okay so now i could use the substitution method right i have g equals this whole big equation so i could take that whole big equation and plug it into the first equation as my value for g all right so when i do that that's going to leave me with um r equals v squared sine 2 divided by.

01:40 Now instead of putting g, we're going to put this second equation here.

01:45 So that's going to be 2v, oops, sine divided by t, right? all that's under that denominator there.

01:59 And it wants us to essentially solve for v, right? we have to get right now we have our equals it needs to say v equals in our equation okay so we can go ahead and um rewrite this so that it's a little bit easier to read right we could go ahead and multiply everything by this denominator right so if we multiply everything by the denominator right so if we multiply everything by the denominator.

02:39 We would have to do it to r as well, right? we'd have to multiply everything by the denominator.

02:44 And that would give us our new equation, right? we would have r times all of this, right? 2v, sine divided by t equals, and then this is our numerator, v squared, sign.

03:06 All right...

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