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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.
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Solution 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.
Solution 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.
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