sec(A) = 5/3 ⇒ cos(A) = 3/5
Angles A and C are complimentary (they sum to 90°), so
sin(C) = cos(A) = 3/5
since sin(90° - x) = cos(x) for all x, and in turn
csc(C) = 1/sin(C) = 5/3
which factor contributes least to the rate at which a stream deposits sediment?
Solution
To determine the angle of the velocity, we use the following equation.
Tan θ = Vertical velocity ÷ Horizontal velocity
As the particle moves from its initial position to its final position, its vertical velocity decreases at the rate of 9.8 m/s each second. During this time its horizontal velocity is constant. To determine the time when the angle is 45˚, we need to determine the object’s vertical velocity at this angle. Let’s determine the vertical and horizontal components of its initial velocity.
Vertical = 50 × sin 60˚, Horizontal = 50 × cos 60˚ = 25 m/s
Since horizontal velocity is constant, let’s put 25 m/s and 45˚ into the tangent equation.
Tan 45 = Vertical velocity ÷ 25
Vertical velocity = 25 m/s
To determine the time for the vertical velocity to decrease from its initial value to 25 m/s, use the following equation.
vf = vi – a × t
a = 9.8
25 = 50 × sin 60˚ – 9.8 × t
t = (25 – 50 × sin 60˚) ÷ -9.8
This is approximately 1.83 seconds.