Quiz 19 Applications of Vectors

The speed of a powerboat in still water is 47 knots per hour (KPH). The powerboat heads directly west across the Messina River. The river flows north at 3.5 KPH. Find the resulting speed of the powerboat.

• 43.5

• 47

• 47.1

• 50.5

The speed of a powerboat in still water is 47 knots per hour (KPH). The powerboat heads directly west across the Messina River. The river flows north at 3.5 KPH. Find the resulting direction of the powerboat from east.

• $4.3\degree$

• $175.7\degree$

• $85.7\degree$

• $184.3\degree$

A Lear Jet has a speed of 420 mph in still air. Suppose the plane travels east and encounters a 50 mph wind blowing due North. Find the resulting speed of the jet.

• 423 mph

• 470 mph

• 370 mph

• 415 mph

A Lear Jet has a speed of 420 mph in still air. Suppose the plane travels east and encounters a 50 mph wind blowing due North. Find the resulting direction of the jet.

• $6.8\degree$

• $8.5\degree$

• $83\degree$

• $354.2\degree$

A lady is swimming in Lake Michigan. She swims at 3.2 mph,  $32\degree$  north of west. There is a 0.8 mph current running  $17\degree$ east of south. Choose the law of cosines equation that could be used to find the speed of the swimmer accounting for the current.

•  $c^2=0.8^2+3.2^2\ -\ 2\cdot0.8\cdot3.2\cos131$  

•  $c^2=0.8^2+3.2^2\ -\ 2\cdot0.8\cdot3.2\cos49$  

•  $c^2=0.8^2+3.2^2\ -\ 2\cdot0.8\cdot3.2\cos139$  

•  $c^2=0.8^2+3.2^2\ -\ 2\cdot0.8\cdot3.2\cos41$  

A lady is swimming in Lake Michigan.  She swims at 3.2 mph, $32\degree$ north of west.  There is a 0.8 mph current running $17\degree$ east of south.  Find the resulting velocity of her swim in component form.

•  $<-2.47,\ 0.93>$  

•  $<2.47,\ 0.93>$  

•  $<-2.47,\ -0.93>$  

•  $<3.2,\ 0.8>$  

If a child pulls a sled through the snow with a force of 50 N exerted at an angle of  $38\degree$ above the horizontal, find the horizontal component of the force.

• 38 N horizontal

• 39.4 N horizontal

• 30.8 N horizontal

• 50 N horizontal

If a child pulls a sled through the snow with a force of 50 N exerted at an angle of  $38\degree$ above the horizontal, find the vertical component of the force. 

• 30.8 N vertical

• 38 N vertical

• 39.4 N vertical

• 50 N vertical

I went for a walk the other day. I went four avenues east (0.80 miles), then twenty-four streets south (1.20 miles), then one avenue west (0.20 miles), and finally eight streets north (0.40 miles). What distance did I travel on my walk?

• 1 mile

• 2.1 miles

• 2.6 miles

• 3.1 miles

I went for a walk the other day. I went four avenues east (0.80 miles), then twenty-four streets south (1.20 miles), then one avenue west (0.20 miles), and finally eight streets north (0.40 miles). What's my resultant displacement (magnitude and direction relative to due east)?

• 1 mile at $307\degree$ off east.

• 1.5 miles at $307\degree$ off east

• 1 mile at $53\degree$ off east

• 1.5 miles at $53\degree$ off east