Question

Sarah and Kenneth are going to meet partway between their homes and each leave their home at the same time. Sarah drives at 31.0 m/s due east and Kenneth drives 65.0 mph due west. They meet somewhere between their homes after they each have been driving for 29.2 minutes. a.) Draw a diagram showing Sarah and Kenneth's displacement vectors. b.) How far apart are their homes in meters? c.) How far apart are their homes in miles? d.) Did they meet closer to Sarah's home or Kenneth's home?

Answer 1

Answer:

b) 105220.8 m

c) 65.38 miles

d) Kenneth's home

Explanation:

Velocity of Sarah = 31 m/s east

Velocity of Kenneth = 65 mph = 65×(1609.34/3600) m/s west

Time in seconds = 29.2×60 = 1752 s

Displacement = Velocity × time

Displacement of Sarah = 31×1752 = 54312 m

Displacement of Kenneth = 65×(1609.34/3600)×1752 = 50908.8 m

b) So, distance between their homes in meters is 54312 m + 50908.8 m = 105220.8 m

c) Converting to miles

$\frac{105220.8}{1609.34}=65.38\ miles$

Their homes are 65.38 miles apart

d) They met closer to Kenneth's house (50908.8 m)