+1313 Urgent* Two particals, find the velocity for each.
Note: the v1 and v2 are velocities.
17= v1sin(30)+v2sin(-45) Along the x axis.
Substituting in the y axis equation where v2 = v1cos(30)/cos(45)
v2sin(30) -v1cos(30)/cos(45) *cos45 = 17
Solve please.
+33661 I think you might be trying to solve the following equations (from a previous problem):
17 = v1*cos(45) + v2*cos(30) ...(1)
0 = -v1*sin(45) + v2*sin(30) ...(2)
Add v1*sin(45) to both sides of (2) and then divide both sides by sin(45)
v1 = v2*sin(30)/sin(45) ...(3)
Replace v1 in (1) by (3)
17 = v2*sin(30)/sin(45)*cos(45) + v2*cos(30)
Factor the right-hand side
17 = v2*[sin(30)/sin(45)*cos(45) + cos(30)]
Divide both sides by [sin(30)/sin(45)*cos(45) + cos(30)] to get v2
v2 = 17/[sin(30)/sin(45)*cos(45) + cos(30)] ...(4)
Replace v2 in (3) by (4) to get v1
v1 = 17/[sin(30)/sin(45)*cos(45) + cos(30)]*sin(30)/sin(45)
$${\mathtt{v1}} = {\frac{{\frac{{\mathtt{17}}}{\left[{\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{30}}^\circ\right)}\right]}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}} \Rightarrow {\mathtt{v1}} = {\mathtt{8.799\: \!847\: \!533\: \!482\: \!900\: \!7}}$$
$${\mathtt{v2}} = {\frac{{\mathtt{17}}}{\left[{\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{30}}^\circ\right)}\right]}} \Rightarrow {\mathtt{v2}} = {\mathtt{12.444\: \!863\: \!728\: \!674\: \!910\: \!2}}$$
+33661 I think you might be trying to solve the following equations (from a previous problem):
17 = v1*cos(45) + v2*cos(30) ...(1)
0 = -v1*sin(45) + v2*sin(30) ...(2)
Add v1*sin(45) to both sides of (2) and then divide both sides by sin(45)
v1 = v2*sin(30)/sin(45) ...(3)
Replace v1 in (1) by (3)
17 = v2*sin(30)/sin(45)*cos(45) + v2*cos(30)
Factor the right-hand side
17 = v2*[sin(30)/sin(45)*cos(45) + cos(30)]
Divide both sides by [sin(30)/sin(45)*cos(45) + cos(30)] to get v2
v2 = 17/[sin(30)/sin(45)*cos(45) + cos(30)] ...(4)
Replace v2 in (3) by (4) to get v1
v1 = 17/[sin(30)/sin(45)*cos(45) + cos(30)]*sin(30)/sin(45)
$${\mathtt{v1}} = {\frac{{\frac{{\mathtt{17}}}{\left[{\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{30}}^\circ\right)}\right]}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}} \Rightarrow {\mathtt{v1}} = {\mathtt{8.799\: \!847\: \!533\: \!482\: \!900\: \!7}}$$
$${\mathtt{v2}} = {\frac{{\mathtt{17}}}{\left[{\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{30}}^\circ\right)}\right]}} \Rightarrow {\mathtt{v2}} = {\mathtt{12.444\: \!863\: \!728\: \!674\: \!910\: \!2}}$$
