Answer to Question #271345 in Mechanics | Relativity for bookaddict

Question

A turkish composite bow can release an arrow with a speed of 100 m/s.

(a) if a turk were to fire the bow at 10 degrees above the horizontal in order to hit someone lying 5 metres below him, if air resistance is negligible, what would be:

(i) the time taken?

(ii) the horizontal distance x?

(b) repeat the above calculations assuming vertical air resistance is negligible, but horizontally it causes a deceleration of 0.5 m/s².

Answer 1

a)

$t_1=\frac{v\sin\alpha}g=1.77~s,$

$s_1=\frac{v^2\sin2\alpha}{2g}=174.5~m,$

$t_2=\frac{\sqrt{v^2\sin^2\alpha+2gh}}g=2.04~s,$

$s_2=\frac{v\cos\alpha}g\sqrt{v^2\sin^2\alpha+2gh}=200.9~m,$

$t=t_1+t_2=3.81~s,$

$s=s_1+s_2=375.4~m.$

b)

$t_1'=t_1=1.77~s,$

$s_1'=s_1-\frac{at_1^2}2=173.7~m,$

$t_2'=t_2=2.04~m,$

$s_2'=s_2-\frac{at_2^2}2=199.9~m,$

$t'=t=3.81~s,$

$s'=s_1'+s_2'=373.6~m.$