A new circus act is called the Texas Tumblers. Lovely Mary Belle swings from a t

Question

A new circus act is called the Texas Tumblers. Lovely Mary Belle swings from a trapeze, projects herself at an angle of 53 ^circ, and is supposed to be caught by Joe Bob, whose hands are 6.1 { m m} above and 8.2 { m m} horizontally from her launch point (the figure (Figure 1) ). You can ignore air resistance. What initial speed v_0 must Mary Belle have just to reach Joe Bob? Express your answer using three significant figures. v_0 = 13.8 Part B For the initial speed calculated in part A, what is the magnitude of her velocity when Mary Belle reaches Joe Bob? Express your answer using three significant figures. v = 8.42 Part C For the initial speed calculated in part A, what is the direction of her velocity when Mary Belle reaches Joe Bob? Express your answer using two significant figures. phi = 9.2 Part D Assuming that Mary Belle has the initial speed calculated in part A, draw x(t) graph showing the motion of Mary Belle. Your graph should show the motion up until the point where Mary Belle reaches Joe Bob. Assume x = 0 is the trapeze where Mary Belle swings and t = 0 when she projects herself. SubmitMy AnswersGive Up Try Again; 3 attempts remaining Part E Assuming that Mary Belle has the initial speed calculated in part A, draw y(t) graph showing the motion of Mary Belle. Your graph should show the motion up until the point where Mary Belle reaches Joe Bob. Assume y = 0 is the trapeze where Mary Belle swings and t = 0 when she projects herself. SubmitMy AnswersGive Up Try Again; 4 attempts remaining Part F Assuming that Mary Belle has the initial speed calculated in part A, draw v_x(t) graph showing the motion of Mary Belle. Your graph should show the motion up until the point where Mary Belle reaches Joe Bob. SubmitMy AnswersGive Up Try Again; 2 attempts remaining Part G Assuming that Mary Belle has the initial speed calculated in part A, draw v_y(t) graph showing the motion of Mary Belle. Your graph should show the motion up until the point where Mary Belle reaches Joe Bob. SubmitMy AnswersGive Up Correct Part H The night of their debut performance, Joe Bob misses her completely as she flies past. How far horizontally does Mary Belle travel, from her initial launch point, before landing in the safety net 8.6 { m m} below her starting point? Express your answer using two significant figures.

Explanation / Answer

A From the ballistic curve eq, 2V² = -gsec²T*x²/(y - xtanT) I get V = 14 m/s B Vh = 14*cos53° = 8.425 m/s Vvi = 14*sin53° = 11.18 m/s Vv² = Vvi² - 2gy ? Vv = 2.33 m/s V = v(Vh²+Vv²) = 8.7 m/s (you forgot to include the vertical velocity) C She is going 2.33 m/s up and 8.435 m/s horizontally, so her angle above horizontal is: T = arctan(2.33/8.425) = 15.46° There is no reason to assume that she is at the top of her trajectory when she makes contact. The expression for Vv above shows that she still has some vertical KE left when she meets JB.

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