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Question

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Find the vectors T, N, and B at the given point. r(t) = 2 cost, 2 sin t, 2 In cost (2, 0, 0) This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. A ball is thrown at an angle of 45 degree to the ground. If the ball lands 91 m away, what was the initial speed of the ball? (g 9.8 m/s2) From Equations 4, for a projectile fired at angle of elevation alpha with initial speed v0, the position vector is given by r(t) = (v0 cos alpha)ti + [(v0 sin alpha)t - 1/2 gt2]j. Since our ball is thrown at angle of elevation alpha = 45 degree, its position vector is r(t) = (v0 cos 45 degree)ti + (v0 sin 45 degree)t - 1/2gt2]j, which evaluates to r(t) = v0ti + v0t - 1/2 gt2 j.

Explanation / Answer

T(t)=r'(t)/|r'(t)|.. r'(t)= |r'(t)|=sqrt(4sin^2 t+4cos^2 t + 4tan^2 t)=sqrt(4+4tan^2 t)=2sec t...... hence T(t)= .......... N(t)=T'(t)/|T'(t)|=/sqrt(1+cos^2 t

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