a$)$ A person michally at vert on a flat jloar throws a ball upward at

an angle of $=45$ with withal speed $V_0=12mls.$ He catcher the

ball $T$ rectouds later by accelocahng with accelcrubon $a_1=24t^2$

for the just $\frac{1}{3}T$ seconds and then with constant accelerahon

$C_2$ for the remaming $\frac{2}{3}T$ seconds. He catcher the ball at

the same haight he turew the ball.

$($i$)$ Write the equahons of motion of the ball and use them

to find the time of flight $T$ and the renge $R$ of the

ball.

$($ii$)$ Fuid the velocity and dotance cavered by the person at

$t=\frac{1}{3}T.$

$($iii$)$ Use your answer in $($ii$)$ to find the total distance

covered by the person grom the time he threw the ball

to when he atches it in terms of the conrtant

acceleration $a_2.$

$($iv$)$ Deduce from your awswers of $($i$)$ and $($iii$),$ the value

of the conotant accelerahus $=>.$