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Katena32 [7]
3 years ago
13

Jeff of the Jungle swings on a 7.6-m vine that initially makes an angle of 32 ∘ with the vertical.

Physics
1 answer:
shtirl [24]3 years ago
3 0

To solve this problem we will use the trigonometric concepts to find the distance h, which will allow us to find the speed of Jeff and that will finally be the variable that will indicate the total tension, since it is the variable of the centrifugal Force given in the vine at the lowest poing of the swing.

From the image:

cos (32) = \frac{(7.6-h)}{7.6}

h = 1.1548m

When Jeff reaches his lowest point his potential energy is converted to kinetic energy

PE = KE

mgh = \frac{1}{2} mv^2

v = \sqrt{2gh}

v = \sqrt{2(9.8)(1.1548)}

v= 4.75m/s

Tension in the string at the lowest point is sum of weight of Jeff and the his centripetal force

T = W+F_c

T = mg + \frac{mv^2}{r}

T = (83)(9.8)+\frac{(9.8)( 4.75)^2}{7.6}

T = 842.49N

Therefore the tension in the vine at the lowest point of the swing is 842.49N

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Answer:

(a). The height of the cliff is 41.67 m.

(b). The maximum height of the ball is 41.67 m

(c). The ball's impact speed is 16.52 m/s.

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Put the value into the formula

v=\sqrt{(16.5)^2+(-0.82)^2}

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(b). The maximum height of the ball is 41.67 m

(c). The ball's impact speed is 16.52 m/s.

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