CEN$211($ Dynamics $-$ HW$1)$

$1\mathrm{.}11$ A ball is tossed with a velocity of $10\frac{m}{s}$ directed vertically upward from a window located $20$ m above the ground. Knowing that the acceleration of the ball is constant and equal to $9\mathrm{.}81\frac{m}{s}2$ downward, determine $(a)$ the velocity $v$ and elevation $y$ of the ball above the ground at any time $t,(b)$ the highest elevation reached by the ball and the corresponding value of $t,(c)$ the time when the ball will hit the ground and the corresponding velocity.

$12-135.$ When $t=0,$ the train has a speed of $8\frac{m}{s},$ which is increasing at $0\mathrm{.}5\frac{m}{s^2}.$ Determine the magnitude of the acceleration of the engine when it reaches point $A,$ at $t=20s.$ Here the radius of curvature of the tracks is ${}_A=400m.$