Velocities. please help?

Question

1. A passenger on a boat moving at 1.50m/s on a still lake walks up a flight of stairs at a speed of 0.50m/s. The stairs are angled at 45º pointing in the direction of motion to the right. What is the velocity of the passenger relative to the water?

2. An unmarked police car, travelling a constant 95km/h, is passed by a speeder travelling 145km/h. precisely 1.00s after the speed passes, the policeman steps on the accelerator. If the police car’s acceleration is 2.00m/s², how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?

Answer 1

1)

The passenger velocity with respect to the boat = 0.5cos 45

V pass = 0.353 m/s

Velocity of passenger with respect to the water = 1.5+0.353=

1.853 m/s

2)

145 km/h = 40.27 m/s

95 km/h = 26.3 m/s

Let X = the distance travelled by both the Speeder and the policeman when he catches up with the speeder!

X s = Vs*t = 40.27 *t

Xp = 26.3*(t-1) +0.5*2*(t-1)^2

Xs and Xp = the distance covered by both the speeder and the policeman

40.27t= 26.3t-26.3 +t^2-2t+1

t^2 -15.97t-25.3=0

t = 17.42

t = 17.42 seconds. This is the time it takes the police to catch up with the speeder!