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(C) Given: Mass $m = 5\,kg$,initial velocity $\vec{u} = 30\hat{i} + 40\hat{j}\,m/s$,and force $\vec{F} = -1\hat{i} - 5\hat{j}\,N$.We are interested in

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$40$

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(C) Given: Mass $m = 5\,kg$,initial velocity $\vec{u} = 30\hat{i} + 40\hat{j}\,m/s$,and force $\vec{F} = -1\hat{i} - 5\hat{j}\,N$.We are interested in the $y$-component of the motion.The initial $y$-component of velocity is $u_y = 40\,m/s$.The $y$-component of the force is $F_y = -5\,N$.Using Newton's second law,the acceleration in the $y$-direction is:$a_y = \frac{F_y}{m} = \frac{-5\,N}{5\,kg} = -1\,m/s^2$.Using the first equation of motion $v_y = u_y + a_y t$,we set the final $y$-velocity $v_y = 0$:$0 = 40 + (-1)t$$t = 40\,s$.Therefore,the time taken for the $y$-component of the velocity to become zero is $40\,s$.

$A$ body of mass $5\, kg$ starts from the origin with an initial velocity $\vec{u} = 30\hat{i} + 40\hat{j}\,m/s$. If a constant force $\vec{F} = -(\hat{i} + 5\hat{j})\,N$ acts on the body,the time in which the $y$-component of the velocity becomes zero is ......... $s$.

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