You're sailboarding at 7.0 m/s when a wind gust hits, lasting 6.3 s accelerating your board at 0.51 m/s2 at a 35∘ to your original direction.
a) Find the magnitude of displacement during the gust.
b) Find the direction of your displacement during the gust.
displacement=sqrt((7*6.3)^2+(1/2 .51 * 6.3^2)^2 )
displacement=arc cos 7*6.3/(.5*.51*6.3^2)
Can you put the second displacement equation in a better form? Im not understanding what to multiply and divide (add more parentheses).
To find the answers to these questions, we need to use the principles of physics, specifically the kinematic equations. Let's break down the problem step by step.
Step 1: Find the initial velocity
Given: Initial speed while sailboarding = 7.0 m/s
Since there is no information about its direction, we can assume it is in the same direction as the displacement during the gust.
Step 2: Find the final velocity
The final velocity can be found using the equation:
vf = vi + at
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Given: Acceleration during the gust = 0.51 m/s^2
Time the gust lasts = 6.3 s
vf = 7.0 m/s + (0.51 m/s^2)(6.3 s)
Step 3: Find the magnitude of displacement
The magnitude of displacement can be found using the equation:
d = ((vi + vf)/2) * t
where d is the displacement, vi and vf are the initial and final velocities, and t is the time.
d = ((7.0 m/s + vf)/2) * 6.3 s
Step 4: Find the direction of displacement
Given: The gust accelerates the board at a 35° angle to the original direction.
To find the direction of displacement, we need to add the angle of acceleration to the original direction.
Now let's plug in the given values and solve the equations.
Step 1: Initial velocity
vi = 7.0 m/s
Step 2: Final velocity
vf = 7.0 m/s + (0.51 m/s^2)(6.3 s)
Step 3: Magnitude of displacement
d = ((7.0 m/s + vf)/2) * 6.3 s
Step 4: Direction of displacement
Add the 35° angle to the original direction.
Now you can calculate the answers to both parts (a) and (b) of the question.