Motion of cars

The route from Zlín to Liberec via Olomouc and Hradec Králové measures s = 300 km.
a) Mr. Horák set out from Zlín at time tH = 16:00 h with a truck at an average speed of vH = 40 km/h.
At time tN = 17:30 h, Mr. Novák set out after him by car with an average speed of vN = 55 km/h. How far from Zlín did they meet? Near which larger city was it?
c) Simultaneously with Mr. Horák, Mr. Skalák set out at 16:00 h in the opposite direction along the route from Liberec to Zlín and with his vehicle he moved at an average speed of 50 km/h. When and how far from Liberec did he meet with Mr. Horák?
d) Draw into one graph the motion of all three cars as a function of time, and read from the graph the times and also the places of meeting from parts a) and d). Who will arrive at the destination first?

Final Answer:

a =  161.0526 km
b =  166.6667 km

Step-by-step explanation:

s=300 km t1=16.00 h v1=40 km/h t2=17.50 h t11=t2t1=17.516=23=1.5 h v2=55 km/h s1+s2 = s v1 t+v2 (tt11)=s=300 t=(s+v2 t11)/(v1+v2)=(300+55 1.5)/(40+55)=381534.0263 h s1=v1 t=40 4.0263=193060161.0526 km s2=ss1=300161.0526=192640138.9474 km  a=s1=161.0526=161.0526 km
v3=50 km/h s3+s4 = s v1 t3 + v3 t3 = s t3=s/(v1+v3)=300/(40+50)=3103.3333 h s3=v1 t3=40 3.3333=3400133.3333 km s4=v3 t3=50 3.3333=3500166.6667 km  b=s4=166.6667=166.6667 km



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