Answer
a) $\approx 3591m$
b) $\approx 1631m$
c) 205 m/s or 204.8 m/s
Work Step by Step
(a) As we are given that $v_0=200 m/s$ and $\theta =60^\circ$
Then $v(t)=\lt 200 \cos 60^\circ, 200 \sin 60^\circ-9.8 t\gt$
or, $v(t)=\lt 100 ,100 \sqrt3-9.8 t\gt$
Also, $r(t)=\int v(t) dt$
or, $r(t)=\int [\lt 100 ,100 \sqrt3-9.8 t\gt]dt$
or, $r(t)=\lt 100t ,100 \sqrt3t-4.9t^2\gt$
Hence, $t=35.915$
Thus, Range: $R=35.915 * 100 \approx 3591 m$
(b) As we are given that $v_0=200 m/s$ and $\theta =60^\circ$
See part (a), which says that $t=35.915$
Hence, Maximum height$=100+1531 \approx 1631 m $
(c) As we are given that $v_0=200 m/s$ and $\theta =60^\circ$
Need to find Horizontal Speed .
Thus, $s(t)=|v(t)|=\sqrt{(100)^2+(100 \sqrt3-9.8 (35.915))^2}$
or, $s(t)=205 m/s$ or 204.8 m/s
