Answer to Question #229662 in Physics for April

Question #229662

A bullet is fired at an angle of 30° above the horizontal with a velocity of 600m/s. Find the range the time it returns to the same level and the position and velocity of the bullet 40 s after after it is fired


1
Expert's answer
2021-08-25T17:24:11-0400

Given:

v0=600m/sv_0=600\:\rm m/s

θ=30\theta=30^{\circ}

t1=40st_1=40\:\rm s


The range

R=v02sin2θg=6002sin609.8=31813mR=\frac{v_0^2\sin2\theta}{g}=\frac{600^2\sin 60^{\circ}}{9.8}=31813\:\rm m

The time of motion

t=2v0sinθg=2600sin309.8=61st=\frac{2v_0\sin\theta}{g}=\frac{2*600\sin 30^{\circ}}{9.8}=61\:\rm s

After 40 s

x=v0cosθt1=600cos3040=20784mx=v_0\cos\theta *t_1=600\cos 30^{\circ}*40=20784\:\rm m

y=v0sinθt1gt122y=v_0\sin\theta *t_1-\frac{gt_1^2}{2}

y=600sin30409.84022=4160my=600\sin 30^{\circ}*40-\frac{9.8*40^2}{2}=4160\:\rm m

The speed of a bullet

v=(v0cosθ)2+(v0sinθgt1)v=\sqrt{(v_0\cos\theta)^2+(v_0\sin\theta-gt_1)}

v=(600cos30)2+(600sin309.840)2=528m/sv=\sqrt{(600\cos 30^{\circ})^2+(600\sin30^{\circ}-9.8*40)^2}\\=528\:\rm m/s


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