Question

The tangential acceleration of the tip of a blade is $47.13m/s^2$ and its centripetal acceleration is $473.9m/s^2$. Find the value of linear acceleration of the tip of the blade. (in $m/s^2$)

• A. $5\times {10}^2$
• B. $4.762\times {10}^2$
• C. $4.762\times {10}^3$
• D. $4.762\times {10}^5$

Answer 1

The correct option is B $4.762\times {10}^2$

The linear acceleration will be resultant of tangential acceleration and centripetal acceleration and angle between both is $\frac{\pi }{2}$.

So the linear acceleration is given by

$a_{linear}=\sqrt{a_t^2+a_c^2}=\sqrt{(473.9{)}^2+(47.13{)}^2}=4.762\times {10}^{2}m/s^2$