Answer:
case x py L is in the positive z direction
case y px L the negative z direction
Explanation:
The angular amount is defined by the relation
L = r x p
the bold are vectors, where r is the position vector and p is the linear amount vector.
The module of this vector can be concentrated by the relation
L = r p sin θ
the direction of the vector L can be found by the right-hand rule where the thumb points in the direction of the displacement vector, the fingers extended in the direction of the moment p which is the same direction of speed and the palm points in the direction of the angular momentum L
in the case x py
the thumb is in the x direction, the fingers are extended in the direction and the palm is in the positive z direction
In the case y px
the thumb is in the y direction, the fingers are in the x direction, the palm is in the negative z direction
Assume no air resistance, and g = 9.8 m/s².
Let
x = angle that the initial velocity makes with the horizontal.
u = 30 cos(x), horizontal velocity
v = 30 sin(x), vertical launch velocity
The horizontal distance traveled is 55 m, therefore the time of flight is
t = 55/[30 cos(x)] = 1.8333 sec(x) s
With regard to the vertical velocity, and the time of flight,obtain
[30 sin(x)]*(1.8333 sec(x)) + (1/2)*(-9.8)*(1.8333 sec(x))² = 0
55 tan(x) - 16.469 sec²x = 0
55 tan(x) - 16.469[1 + tan²x] = 0
16.469 tan²x - 55 tan(x) + 16.469 = 0
tan²x - 3.3396 tan(x) + 1 = 0
Solve with the quadratic formula.
tan(x) = 0.5[3.3396 +/- √(7.153)] = 3.007 or 0.3326
Therefore
x = 71.6° or x = 18.4°
The time of flight is
t = 1.8333 sec(x) = 5.8096 s or 1.932 s
The initial vertical velocity is
v = 30 sin(x) = 28.467 m/s or 9.468 m/s
The horizontal velocity is
u = 30 cos(x) = 9.467 m/s or 28.469 m/s
If t = 5.8096 s,
u*t = 9.467*5.8096 = 55 m (Correct)
or
u*t = 28.469*15.8096 = 165.4 m (Incorrect)
Therefore, reject x = 18.4°. The correct solution is
t = 5.8096 s
x = 71.6°
u = 9.467 m/s
v = 28.467 m/s
The height from which the ball was thrown is
h = 28.467*5.8096 - 0.5*9.8*5.8096² = -110.4 m
The ball was thrown from a height of 110.4 m
Answer: h = 110.4 m
Always here to help. Bring it!!!
The answer is, "the speed of the current is 5 miles per hour."
To calculate the speed of the current,
let's assume speed of current = xmph. Time taken to travel from one pier to another with the current = 100/(20+x)h
But the time taken to travel from one pier to another with the current, which is given is = 4 hours. So, 4=100/(20+x) 80+4x = 100
4x = 20
x = 5 Thus, the speed of the current is 5 miles per hour.
