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)| = \(\displaystyle \sqrt{(85)^{2} + (85|\sqrt{3} - 9.8(30.04577931))^{2}} = 170\)

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

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

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

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

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

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

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

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

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

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

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

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