You're sailboarding at 6.1m/s when a wind gust hits, lasting 6.3s accelerating your board at 0.48m/s2 at a 35∘ to your original direction
To calculate the final velocity of the sailboard after the wind gust, we can use the kinematic equation:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case:
u = 6.1 m/s (initial velocity)
a = 0.48 m/s² (acceleration)
t = 6.3 s (time)
First, we need to break down the acceleration into its horizontal and vertical components. Since the angle is given as 35° to the original direction, we can find the horizontal component of acceleration using trigonometry:
a_horizontal = a * cos(angle)
Substituting the values:
a_horizontal = 0.48 m/s² * cos(35°)
Next, calculate the change in horizontal velocity during the time the wind gust lasts using the kinematic equation:
Δv_horizontal = a_horizontal * t
Substituting the values:
Δv_horizontal = (0.48 m/s² * cos(35°)) * 6.3 s
Finally, add the change in horizontal velocity to the initial horizontal velocity to get the final horizontal velocity:
v_horizontal = u_horizontal + Δv_horizontal
Substituting the values:
v_horizontal = 6.1 m/s + (0.48 m/s² * cos(35°)) * 6.3 s
The final horizontal velocity will be v_horizontal.