Question

1. An airplane is traveling 835 km/h in a direction 41.5 ∘ west of north

PART A

Find the components of the velocity vector in the northerly and westerly directions. Enter your answers using three significant figures separated by a comma.

PART B

How far north and how far west has the plane traveled after 4.00 h? Enter your answers using three significant figures separated by a comma.

BOTH QUESTIONS NEED TWO ANSWERS.

2. A football is kicked at ground level with a speed of 17.0 m/s at an angle of 38.5 ∘ to the horizontal.

How much later does it hit the ground?

Express your answer using three significant figures and include the appropriate units.

3. A projectile is fired with an initial speed of 36.5 m/s at an angle of 44.1 ∘ above the horizontal on a long flat firing range.

Determine the maximum height reached by the projectile.

Express your answer using three significant figures and include the appropriate units.

Answer 1

1.velocity along northern direction is, V is the actual velocity and theta (@) is the angle between the actual velocity and positive y axis.

North component velocity = (cos 41.5 x 835) = (1.4 x 625.178) = 625.378 km/h
West component velocity = (sin 41.5 x 835) = 553.2877 km/h

after 4 hour distance covered by north coponent =625.378*4=2501.512

after 4 hour distance covered by south coponent=553.2877*4=2213.1508

so Dnorth-Dsouth= 2501.512-2213.1508288.36km

2.by equation we have

y= vsin(@)t+ 0.5 at^2

for hitting the ground y=0

which gives t= -2vsin(@)/g

here g= -9.8m/s (g is acting downbard)

t=2.159 sec

3. Hmax= vsin(@)^2/2g

   =(36.5sin(44.1))^2/2(9.8)

   =32.918m