1 a)The fastest animal on Earth is the peregrine falcon, which can reach speeds of 390 km/h when diving in free fall. Assuming that the bird starts from rest as it began its dive, over what vertical displacement would it travel to reach its maximum speed?

b) A cruise ship is travelling at 12.5m/s E heading towards the docking station that is approximately 1.0Km away. If the ship slows down with a maximum rate of 0.08m/s (w) will the ship come to a stop at the right time? Justify your answer with calculation ?

 

1a)

The peregrine falcon reaches its maximum speed when all of its potential energy has been fully converted into kinetic energy

The formula for potential energy, PE = mgh,

The formula for kinetic energy, KE = 0.5mv²

By conservation of energy,

KE = PE

mgh = 0.5mv²

gh = 0.5v², solving for the vertical displacement h, given the velocity, we must convert it to m/s for consistency of units

h = 0.5v²/g = 0.5(390 km/h * 1hr/3600s *1000m/km)/9.81 = 5.52 m

1b)

Given:

Initial velocity of ship: v_i = 12.5 m/s

Since we want it to stop, final velocity of ship: v_f =0 m/s

maximum deceleration = a = -0.08 m/s

Using the kinematic equation,

v_f² = v_i² + 2a????x

Plugging in our values,

0 = 12.5² + 2(-0.08)????x

????x = -(12.5)²/(-0.08) = 1953 m = 1.953 km

Since the required distance for the ship to fully stop is 1.953 km and this is greater than the distance from the docking station, the ship would not be able to come to a stop at the right time.