Two dimensional kinematics help help help please. thanks?

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.

If x' and y' are the horizontal and vertical components of velocity relative to water:

x' = 1.50 + 0.50 cos(45)

= 1.85 m/s.

y' = 0.50 sin(45)

= 0.354 m/s.

The resultant is sqrt[ (x')^2 + (y')^2 ]

= 1.89 m/s. at angle a to the horizontal where:

tan(a) = y' / x'

a = 10.8 deg.

2.

95 km/h = 26.389 m/s.

145 km/h = 40.278 m/s.

t sec. after the speeder passes the police car, his distance in metres from the police car's position at t = 0 is:

40.278t

The police car's distance from the same base point for time t >= 1 sec. is:

26.389 * 1 + 26.389(t - 1) + 2.00(t - 1)^2 / 2

The police car overtakes the speeder when:

26.389 * 1 + 26.389(t - 1) + 2.00(t - 1)^2 / 2 = 40.278t

t^2 - 2t + 1 + 26.389t - 40.278t = 0

t^2 - 15.889t + 1 = 0

t = (15.889 + sqrt(15.889^2 - 4)) / 2

= 15.8 sec.