# Speed at Impact - # 2

#### Jason76

A projectile is fired with an initial speed of 170 m/s and angle of elevation of 60 degrees. Find speed at impact. $$\displaystyle t = 42.4175707974285$$

$$\displaystyle y(t) = v_{0}\sin\theta - 4.9t^{2}$$

$$\displaystyle y(t) = 170\sin(60)t - 4.9t^{2} + 100$$

$$\displaystyle y'(t) = 170\sin(60) - 9.8t$$

$$\displaystyle y'(t) = 85\sqrt{3} - 9.8t$$

$$\displaystyle x(t) = v_{0}\theta (t)$$

$$\displaystyle x(t) = 170\cos(60)t$$

$$\displaystyle x'(t) = 170\cos(60)$$

$$\displaystyle x'(t) = 85$$

$$\displaystyle r(t) = <170\cos(60)t, 170\sin(60)t - 4.9t^{2}>$$

$$\displaystyle r'(t) = <85, 85\sqrt{3} - 9.8t>$$

|r'(t)| = $$\displaystyle \sqrt{(85)^{2} + (85|\sqrt{3} - 9.8(30.04577931))^{2}} = 170$$

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#### topsquark

Forum Staff
A projectile is fired with an initial speed of 170 m/s and angle of elevation of 60 degrees. Find speed at impact. $$\displaystyle t = 42.4175707974285$$

$$\displaystyle y(t) = v_{0}\sin\theta - 4.9t^{2}$$

$$\displaystyle y(t) = 170\sin(60)t - 4.9t^{2} + 100$$

$$\displaystyle y'(t) = 170\sin(60) - 9.8t$$

$$\displaystyle y'(t) = 85\sqrt{3} - 9.8t$$

$$\displaystyle x(t) = v_{0}\theta (t)$$

$$\displaystyle x(t) = 170\cos(60)t$$

$$\displaystyle x'(t) = 170\cos(60)$$

$$\displaystyle x'(t) = 85$$

$$\displaystyle r(t) = <170\cos(60)t, 170\sin(60)t - 4.9t^{2}>$$

$$\displaystyle r'(t) = <85, 85\sqrt{3} - 9.8t>$$

|r'(t)| = $$\displaystyle \sqrt{(85)^{2} + (85|\sqrt{3} - 9.8(30.04577931))^{2}} = 170$$
A couple of points. Yes, v = 170 m/s.

The problems I see are this: Your table of equations is wrong, for the same reasons I said they were wrong in the other post. You have a t = 42..... which is clearly from the other problem and not this one, and your second equation has a 100 in it that also is from the other problem.

Given these problems I really can't tell how you got the correct answer.

I've said this before: Organize your work and do it step by step. Write everything down and don't skip steps. Clarity is your ally on an exam!

-Dan

1 person

#### Jason76

A couple of points. Yes, v = 170 m/s.

The problems I see are this: Your table of equations is wrong, for the same reasons I said they were wrong in the other post. You have a t = 42..... which is clearly from the other problem and not this one, and your second equation has a 100 in it that also is from the other problem.

Given these problems I really can't tell how you got the correct answer.

I've said this before: Organize your work and do it step by step. Write everything down and don't skip steps. Clarity is your ally on an exam!

-Dan
I agree a lot was copy and paste, as the problems are so similar. Nonetheless, as you said, organization can throw someone off the exam. Also, on this online homework, the final value of t plugged in had to be the whole decimal to get the right answer, more than just 1 place or less.