Question

a) On a hot summer day, a young girl swings on a rope above the local swimming hole. When she lets go of the rope her initial velocity is 3.2 m/s at an angle of 35.0∘ above the horizontal. If she is in flight for 0.620 s , how high above the water was she when she let go of the rope? Give your answer to one decimal place

b) A football game begins with a kickoff in which the ball travels a horizontal distance of 38.7 m and lands on the ground. Suppose the ball is punted from an initial height of 0.780 m. If the ball was kicked at an angle of 37.0° above the horizontal, what is the initial speed of the ball in this case? Give your answer to one decimal place.

Answer 1

Considering motion along vertical

h = ho + u sin x * t - 0.5* gt^2

0 = ho + 3.2 sin 35 * 0.62 - 4.9* 0.62^2

ho = 0.746 m

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considering motion along horizontal

R = u cos x * t

ut = 38.7 / cos 37

ut = 48.457

considering motion along vertical

h = ho + u sin x * t - 0. 5* gt^2

0 = 0.78 + (ut) * sin 37 - 4.9* t^2

0 = 0.78 + 48.457* sin 37 - 4.9 t^2

t = 2.47

putting in (i)

u = 19.6 m/s

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