You drive 109 km/h east for 31 min , then 82 km/h north for 42 min . Let the +x-axis point east and the +y-axis north.
A)Find your average velocity for the entire trip.
B)Find your average speed for the entire trip.
You should probably do part b first. Find the vertical component of velocity, then find the time for the ball to reach its maximum height. The total time for the ball to go up and down is twice the time to go up.
Since this is physics, I assume you use SCI units, meters, seconds, newtons, kilograms ...
x direction
31min * 60 s/min = 1860 seconds
u = x velocity = 109000meters/3600 seconds
=30.3 meters/second
x displacement component = 30.3*31*60 = 56,358 meters
y direction
83,000/3600 = 23 m/s
y displacement component =
23* 42*60 = 58,100
distance = sqrt(56,358^2+58,100^2)
= 80,943 meters
time = 73*60 = 4380 seconds
tan angle above x axis (north of east) = 58100/56358
so
angle north of east = 45.8 degrees above x axis
speed = distance/time
= 80,943/4380 = 18.5 m/s
so
Velocity is
18.5 m/s at 45.8 degrees above x axis
18.5 m/s = 66.5 km/h by the way
speed for trip is the sum of the two distances/total time
114,458/4380 = 26.1 m/s
= 94 km/h