A diver springs upward from a three-meters board. At the instant she contacts th
ID: 1490052 • Letter: A
Question
A diver springs upward from a three-meters board. At the instant she contacts the water her speed is 8.90 m/s and her body makes an angle of 75.0 degree with respect to the surf ace of the water. Determine her initial velocity (magnitude and direction). How much time does she spend in the air? Find the acceleration of the system shown if there is no friction. If the coefficient of kinetic friction is 0.33. Take M = 7.5 kg, m = 2.5 kg. A cookie jar is moving up a 40.0 degree incline. At a point 0.50 m from the bottom incline (measured along the incline), it has a speed of 1.5 m/s. The coefficient kinetic friction between jar and incline is 0.15.Explanation / Answer
1) We have: Height h = 3 m, Speed at contact v = 8.9 m / s
The horizontal component of velocity at the time of contact v ' = v cos 75
= 2.303 m / s
The Vertical component of velocity at the time of contact v" = v sin 75
=8.596 m / s
Let the initial velocity u the angle with horizontal then
u cos = v '
= 2.303 ----( 1)
In vertical direction :
Initial velocity U = u sin
final velocity V = v"= 8.596 m / s
distance S = -3 m
accleration a = - g
from the relation V ^ 2 - U ^ 2 = 2aS
8.596^2- U ^ 2 = -2g* -3
= 6g = 58.8
U ^ 2 = 15.09
U = 3.884
u sin = 3.884 ---( 2)
eq ( 2 ) / eq ( 1 ) ==> u sin / u cos = 3.884 / 2.303
tan =1.6868
= 59.4 degrees
fro eq ( 1 ) , initial velocity u = 2.303 / cos59.33
= 4.52 m / s
And spends 0.35 s
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