Answer to Question #134309 in Physics for Rancis B. Wood

Question

A ball is batted into the air and caught at a point 100 m distance horizontally in 4.0 seconds. Neglecting air resistance. Find the maximum height attain by the ball.

A cannon is fired with a muzzle velocity of 300 m/s, at angle of 60 degrees. Find the range, time of flight, maximum height attain.

Answer 1

(i)

$t=\frac{2v_0\sin\alpha}{g}\to \frac{2v_0\sin\alpha}{g}=4 \to v_0\sin\alpha=2g$

$l=\frac{2v_0^2\cos\alpha\sin\alpha}{g}\to \frac{2v_0^2\cos\alpha\sin\alpha}{g}=100$

$h=\frac{v_0^2\sin^2\alpha}{2g}=\frac{(v_0\sin\alpha)^2}{2g}=$

$=\frac{(2g)^2}{2g}=2g=2\cdot9.81=19.62(m)$

(ii)

$l=\frac{2v_0^2\cos\alpha\sin\alpha}{g}=l=\frac{v_0^2\sin2\alpha}{g}=$

$\frac{300^2\cdot\sin(2\cdot60°)}{9.81}=7945(m)$

$t=\frac{2v_0\sin\alpha}{g}=t=\frac{2\cdot300\sin60°}{9.81}\approx53(s)$

$h=\frac{v_0^2\sin^2\alpha}{2g}=\frac{300^2\cdot\sin^260°}{2\cdot9.81}=3440(m)$