velocity height displacement

Question

1.1 A light aircraft, with an air speed of 200 km/h, sets course North 20 0 East. The aircraft is blown off course by a wind of 40 km/h from South 50' East. Calculate the following: 1.1.1 The resultant velocity in magnitude and direction 1.1.2 The displacement of the aircraft after 3 hours in kilometres 1.2 A bullet is fired at a muzzle velocity of 125 m/s at an angle of 25° to the horizontal. Calculate the following: 1.2.1 The horizontal distance of the bullet after 8 seconds 1.2.2 The maximum height of the bullet 1.3 Two ships leave Cape Town harbour simultaneously. Ship K sails North West at 50 km/h and ship L sails South West at 70 km/h. Calculate the velocity of ship L relative to the velocity of ship K in magnitude and direction.

Answer 1

1.2)

Horizontal angle θ = 25°

The initial velocity of the bullet  v₀ =  125 m/s

1.2.1)

The horizontal displacement reached by the bullet after 8sec can be evaluated by following formula 

Horizontal displacement s = v₀ cosθ t  .

s = 125 (cos 25)(8)   

s = 906.307 m 

The horizontal displacement reached by the bullet after 8sec  is 906.307 m .

Answer 2

1.2.2)

Horizontal angle θ = 25°

The initial velocity of the bullet  v₀ =  125 m/s

Earth gravity g = 9.8 m/s

The maximum height reached by the bullet H_max can be evaluated by following formula 

Maximum height H_max = (v₀²sin²θ)/2g

H_max = (125²sin²25) / (2×9.8)

H_max = (15625×0.1786) / (19.6)

H_max = 142.38 m 

So the maximum height of the bullet is 142.38 m .

Answer 3

1.3)

The  ship K  sails at rate of 50 km/h in north west direction .

The  ship L  sails at rate of 70 km/h in south west direction .

So the relative velocity  can be determined by the below diagram .

The obtained triangle is right angled triangle .

Using Pythagoras theory of triangles 

(relative velocity )² = (velocity of ship K )² +  (velocity of ship L )²

(relative velocity )² = 50² + 70²

(relative velocity )² = 7400

Relative velocity = 86.023 km/h .

 The direction of ship K with respect to ship L is 90° .