You're sailboarding at 6.1m/s when a wind gust hits, lasting 6.8s accelerating your board at 0.49m/s2 at a 35∘ to your original direction.
1. Find the magnitude of your displacement during the gust.
Express your answer using two significant figures.
2. Find direction of your displacement during the gust.
Express your answer using two significant figures.
Displacement=Vi*time+ 1/2 a*t^2
D=6.1i+ (.49)(cos35i+sin35j)
figure that up, take the square root of the sums of squares of the i components and j components.
Direction: arctan=jcomponent/icomponent to the leeward of the original course.
2.6m
To find the magnitude of your displacement during the gust, we can use the formula for displacement:
Displacement = Initial Velocity × Time + 1/2 × Acceleration × Time^2
First, we need to calculate the initial velocity during the gust. Since the wind gust is at a 35∘ angle to your original direction, we can find the horizontal component of the initial velocity using trigonometry:
Initial Horizontal Velocity = Initial Velocity × cos(35∘)
Substituting the given values, we have:
Initial Horizontal Velocity = 6.1m/s × cos(35∘)
To calculate the displacement, we then plug in the values:
Displacement = (Initial Horizontal Velocity) × Time + 1/2 × Acceleration × Time^2
= (6.1m/s × cos(35∘)) × 6.8s + 1/2 × 0.49m/s^2 × (6.8s)^2
Calculating this expression will give us the magnitude of your displacement during the gust, expressed with two significant figures.
To find the direction of your displacement during the gust, we can use the tangent of the angle formed by the displacement and the horizontal axis:
Direction = arctan(Displacement / Initial Horizontal Velocity)
Calculating this expression will provide us with the direction of your displacement during the gust, expressed with two significant figures.