Question

Romeo wishes to throw a bouquet of flowers to Juliet, who is on a second-story balcony, at X = 18 m and H = 5.9 m away from his hand. He throws the bouquet at an angle θ = 38 degrees from the horizontal.

a) What should be the initial speed of the bouquet so that it can reach Juliet? (ANSWER: 18 m/s, how?)

b) What maximum height (above Romeo's hand) does the bouquet reach in its flight? (ANSWER: 6.1 m, how?)

c) What is the velocity of the bouquet just before it lands on Juliet's hand? (ANSWER: 14i - 1.8 m/s, how?)

d) Find the average velocity of the bouquet during its flight, in terms of the unit vector i and j. (ANSWER: 14i + 4.6j m/s, how?)

Answer 1

In horizontal direction

x = vt

x = v*cos 38*t

18 = v*cos 38*t

t = 18 / vcos 38

In vertical direction

5.9 = v*sin 38*t - 4.9*t²

5.9 = v*sin 38*(18 / vcos 38) - 4.9*(18 / vcos 38)²

5.9 = 18*tan 38 - 4.9*(18 / vcos 38)²

5.9 - 18*tan 38 = -4.9*(18 / vcos 38)²

-8.16314 = -4.9*(18 / vcos 38)²

v² cos² 38 = 4.9*18*18 / 8.16314

v² cos² 38 = 194.48

v = 17.7 m/s

we can round it off

so,

v =18 m/s

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(b) At maximum height, v_y = 0

so,

h = 1/2 * 9.8 * (18 / 17 * cos 38)

h = 6.18 m

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(c) velocity in x direction won't change

v = x/t

v = 18 / 1.291

v = 14 m/s

In y direction

v_y = 17.7*sin 38 - 9.8*1.291

v_y = -1.8 m/s

so,

v = 14 i - 1.8 j

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(d) As we know velocity in x direction won't change

so,

average velocity will be 14 i + 4,6 m/s