Question

You're sailboarding at 6.0 m/s when a wind gust hits, lasting 6.2 s accelerating your board at 0.46 m/s2 at a 35∘ to your original direction.

A) Find the magnitude of your displacement during the gust. Express your answer using two significant figures.

B) Find direction of your displacement during the gust. Express your answer using two significant figures.

Answer 1

accleration along orginal direction

ax = a cos theta = 0.46 cos 35 = 0.376 m/s^2

ay = a sin theta = 0.46 sin 35 = 0.263 m/s^2

Apply kinematic equation in horizontal

s1= ut + 1/2 at^2

= 6.0(6.2) + 1/2 ( 0.376) (6.2)^2

=44.42 m

in perpendicular

s2= 1/2 at^2

= 0.5 ( 0.263)( 6.2)^2

=5.05 m

total displacment is

x = sqrt s1^2 + s2^2

= sqrt ( 44.42)^2 + (5.05)^2

=44.70 m

rounding two significant x = 45 m

(b)

theta = tan^-1 ( 5.05/44.42) = 6.48 degree

rounding to two significant 6.5 degree

Direction of displacement is 6.5^o from our original velocity in the direction of the 35deg gust