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Motion in a Straight Line

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Question : 5 of 27
Marks: +1, -0
A jet airplane travelling at the speed of 500 km h−1^{-1} ejects its products of combustion at the speed of 1500 km h−1^{-1} relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?
Solution:  
Let vj , vgv_j\ ,\ v_g and v0v_0 be the velocities of jet, ejected gases i.e. combustionproducts and observer on the ground respectively.
Let jet be moving towards right (+ve direction).
∴ Ejected gases will move towards left (–ve direction).
According to the statement
vj=500 km h−1v_{j}=500\ \text{km}\ \text{h}^{-1}
As observer is at ground i.e. at rest
∴ v0=0\therefore\ v_0 = 0
Now relative velocity of plane w.r.t. the observer
vj−v0=500−0=500 km h−1v_{j}-v_{0}=500-0=500\ \text{km}\ \text{h}^{-1}.......(i)
Relative velocity of the combustion products w.r.t. jet plane
vg−vj=1500 km h−1(v_{g}-v_{j}=1500\ \text{km}\ \text{h}^{-1}( given )) .......(ii)
–ve sign indicates that the combustion products move in a directionopposite to that of jet.
∴ Adding equations (i) and (ii), we get the speed of combustionproducts w.r.t. observer on the ground i.e.
 (vj−v0 )+ (vg−vj )\ (v_{j}-v_{0}\ )+\ (v_{g}-v_{j}\ )
=vg−v0=v_{g}-v_{0}
=500+(−1500)=500+(-1500)
or vg−v0v_{g}-v_{0}
=−1000 km h−1=-1000\ \text{km}\ \text{h}^{-1}
–ve sign shows that relative velocity of the ejected gases w.r.t. observer istowards left i.e. –ve direction i.e. in a direction opposite to the motion ofthe jet plane.
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