Question

1) A strong wind blows due east with a constant speed of 50mph. An airplane travels from one city to another which is due north, moving with a speed of 130mph relative to the air. What isthe speed of the airplane relative to the ground?

EXPLAIN the answer please

2) A constant force is exerted on air track cart that is initially at rest on a horizontal air track. Friction between the cart and track is negligible. The force act for a short time interval and gives the cart a certain final speed. To reach the same final speed with a force that is one third as big, the force must be applied for a time interval [....] that of the stronger force.

EXPLAIN the answer please

Answer 1

Q1.

relative speed of plane with respect to ground

=relative speed of plane with repsect to air+releative speed of air with repsect to ground

=130 mph due north + 50 mph due east

magnitude of speed=sqrt(130^2+50^2)=139.2838 mph

direction with east=arctan(speed along north/speed along east)

=arctan(130/50)=68.9625 degrees

hence the speed of air plane with repsect to grounf is 139.2838 mph, 68.9625 degree north of east

Q2.

as we know, impulse applied=change in momentum

==>force*time duration=mass*(final speed-initial speed)

here initial speed=0

let initial force magnitude be F and time duration be T

then F*T=mass*final speed...(1)

now it is given that force has become 1/3rd of the original

hence force=F/3

but final speed remains the same

hence mass*final speed=(F/3)*time

==>F*T=(F/3)*time
==>time=3*T

hence force must be applied for 3 times the original time interval to provide the same final speed