Resolving forces

An aeroplane is flying horizontally and heading north through the air. Its speed through the air is a and the wind is blowing east with a speed b.

The speed over the ground is given by

• $a+b$

• $a^2+b^2$

• $\sqrt{a+b}$

• $\sqrt{a^2+b^2}$

With reference to that same aeroplane, the angle from North at which the plane flies over the ground is given by

• $\cos^{-1}\left(\frac{a}{b}\right)$

• $\sin^{-1}\left(\frac{b}{a}\right)$

• $\tan^{-1}\left(\frac{a}{b}\right)$

• $\tan^{-1}\left(\frac{b}{a}\right)$

The diagram shows the forces acting on a picture, of weight W, suspended by a cord.

The tension in the cord is T. Which of the following expressions shows the correct relationship between W and T?

• $W=2T\cos\theta$

• $W=T\cos\theta$

• $W=T\sin\theta$

• $W=2T\sin\theta$

Read this one carefully:

The diagram shows the forces acting on an object on an inclined surface. The component of R parallel to the inclined surface is

• 0

• W

• $R\cos\theta$

• $R\sin\theta$

Tags

NGSS.HS-PS2-1

With this one, try drawing the diagram yourself to help you if you need it:

A football is kicked at 12 m s^-1 at an angle of 35° to the horizontal. The horizontal component of its velocity, in m s^-1, is given by

• $12\cos\ 35\degree$

• $12\sin35\degree$

• $\frac{12}{\cos35\degree}$

• $\frac{12}{\sin35\degree}$

Again, try drawing the diagram yourself here to help you if you need to:

A model boat is crossing a stream. The stream is travelling east at a speed of 1.5 m $s^{-1}$  .The boat is heading north at a speed of 0.5 m $s^{-1}$  . The magnitude of the resultant velocity is given by

•  $\left(1.5^2+0.5^2\right)\ m\ s^{-1}$  

•  $\sqrt{\left(1.5^2+0.5^2\right)}\ \ m\ s^{-1}$  

•  $\left(1.5\ +0.5\right)\ m\ s^{-1}$  

•  $\sqrt{\left(1.5+0.5\right)}\ m\ s^{-1}$  

Remember, do a diagram if you think it will help:

A body is acted on by a vertical force of 18 N and a horizontal force of 32 N.

The angle to the horizontal of the resultant force is given by

• $\cos^{-1}\left(\frac{18}{32}\right)$

• $\tan^{-1}\left(\frac{18}{32}\right)$

• $\sin^{-1}\left(\frac{32}{18}\right)$

• $\tan^{-1}\left(\frac{32}{18}\right)$

Tags

NGSS.HS-PS2-1

A box of weight 150 N is placed on an inclined plane. The component of the box’s weight acting along the plane is given by W'. What would be the value of W', in Newtons?

• $\frac{150}{\cos15\degree}$

• $150\times\cos15\degree$

• $\frac{150}{\sin15\degree}$

• $150\times\sin15\degree$

Tags

NGSS.HS-PS2-1

A student goes down a slide. Which of the diagrams correctly represents the forces acting on the student?

• A

• B

• C

• D

The diagram above is a free-body force diagram for a hot air balloon when a wind is blowing. The size of the resultant force acting on the balloon is

• 400 N

• 500 N

• 700 N

• 9, 805 N