Question

An ant travels a distance of 8 cm from P to Q and then moves a distance of 6 cm at right angles to PQ. Find its resultant displacement.

Answer 1

We have to find the resultant displacement from the given diagram :

We have: 
PQ = 8 cm and QR = 6 cm
Resultant displacement :
`PR = sqrt(PQ^2 + QR^2)`
= `sqrt(64+36)`
= `sqrt(100)`
= 10 cm
The direction of this displacement is from P to R. If θ is the angle made by PR with PQ then,'
`tan  θ = "RQ"/"PQ"`
⇒ `tan θ = 36/64`
⇒ `θ = tan^-1 0.5625`
⇒ `θ = 29.36^circ`
This is the angle made by the resultant with PQ.

Answer 2

To find the resultant displacement, we treat the movement of the ant as forming a right triangle, where:

• The distance from P to Q is 8 cm (one leg of the triangle).
• The distance moved at a right angle to PQ is 6 cm (the other leg of the triangle).

The resultant displacement is the hypotenuse of this right triangle, which can be calculated using the Pythagorean theorem:

Resultant displacement = `sqrt((8^2 + 6^2)`

Resultant displacement = `sqrt(64+36) = sqrt100 = 10  cm.`

The resultant displacement is 10 cm.