A ball is thrown with an initial velocity of v feet per second, at an angle of θ with the horizontal (see figure in the website below). Find the vertical and horizontal components of the velocity. (Let v = 70 and θ = 40°. Round your answers to two decimal places.)
www.webassign.net/larprecalcrmrp6/6-3-097-alt.gi
vertical component: ? ft/sec
horizontal component: ? ft/sec
vx = v cosθ: 70 cos 40 = 53.623
vy = v sinθ: 70 sin 40 = 44.995
is this correct?
as always,
vx = v cosθ
vy = v sinθ
Oh great, a geometry question! I love playing with angles and velocity. Let me just dust off my clown calculator and get to work.
Now, the vertical component of velocity is given by v * sin(θ). Plugging in the values, we get:
Vertical component = 70 * sin(40°)
Calculating this, we get an answer of approximately 44.81 ft/sec for the vertical component.
Moving on to the horizontal component, it's given by v * cos(θ). Plugging in the values again, we get:
Horizontal component = 70 * cos(40°)
After some calculations, we find that the horizontal component is around 53.51 ft/sec.
So, to summarize:
Vertical component: 44.81 ft/sec
Horizontal component: 53.51 ft/sec
Hope that helps! Keep those balls flying in style.
To find the vertical and horizontal components of the velocity, we can use the following formulas:
Vertical component (Vv) = v * sin(θ)
Horizontal component (Vh) = v * cos(θ)
Given that v = 70 and θ = 40°, we can substitute these values into the formulas:
Vertical component (Vv) = 70 * sin(40°)
Horizontal component (Vh) = 70 * cos(40°)
Calculating:
Vertical component (Vv) = 70 * sin(40°) ≈ 45.14 ft/sec
Horizontal component (Vh) = 70 * cos(40°) ≈ 53.43 ft/sec
Therefore, the vertical component of the velocity is approximately 45.14 ft/sec, and the horizontal component of the velocity is approximately 53.43 ft/sec.
To find the vertical and horizontal components of the velocity, you can use trigonometric functions sine and cosine.
Given:
Initial velocity, v = 70 feet per second
Angle with the horizontal, θ = 40°
To find the vertical component (v_y), you can use the sine of the angle:
v_y = v * sin(θ)
Substituting the given values:
v_y = 70 * sin(40°)
Using a scientific calculator, calculate the value of sin(40°) to get:
v_y ≈ 45.07 ft/sec (rounded to two decimal places)
To find the horizontal component (v_x), you can use the cosine of the angle:
v_x = v * cos(θ)
Substituting the given values:
v_x = 70 * cos(40°)
Using a scientific calculator, calculate the value of cos(40°) to get:
v_x ≈ 53.66 ft/sec (rounded to two decimal places)
So, the vertical component of the velocity is approximately 45.07 ft/sec, and the horizontal component is approximately 53.66 ft/sec.