To find speed of a plane when position of radar is given

[hermy]

Homework Statement

A plane flying at a constant velocity v (parallel to x-axis) at a height h = 8 km is being tracked by a radar located at origin. if the angle A is decreasing at the rate of 0.025 rad/s, the velocity of the plane when A = 60 degrees is: (A is the angle made by the position vector of plane with the x-axis)

a) 1440 km/h
b) 960 km/h
c) 1920 km/h
d) 480 m/h

Homework Equations

vt = h cot A

differentiating w.r.t t (time):

v = h cosec² A (0.025) -------eqn 1

= 0.27 km/h

The Attempt at a Solution

the answer is nowhere near what one would expect. also, if v is consatant then how can it depend on A? (eqn 1) Where am i going wrong?

 

[hermy]

Is this question so tough, or is it unclear?

Any help would be appreciated, pls..

 

[Mentallic]

I was actually really stumped on this question. The maths was telling me there's no solution...
It's because there is a contradiction in the information. The plane can't be flying at constant velocity AND the angle it makes from the radar tower changes constantly too. The question needs fixing up.

 

[Borek]

Perhaps it doesn't state angle changes with a constant speed, but it changes with a given speed when angle is 60 deg?

 

[Mentallic]

Oh yes you're right Borek, the question implies the angle is changing at that rate at the given angle, not constantly (of course)...

Well then the only problem is that your units are incorrect.

It's actually 4/15 km/second, not km/hour.

To realize what units you need for future questions without going through the entire problem using units constantly, just notice that the height is in km, and that the angle was changing at some value in seconds. km/sec.

 

[hermy]

It's actually 4/15 km/second, not km/hour.

that's right, mentallic. so, the answer would be 960 km/h. the answer was supposed to be (b), so that must have been the only mistake in the question. a pretty silly doubt actually, so thanks a lot for taking the trouble to set it right.

and yes, the rate of change of angle must be instantaneous, that seems to be the only way v can be constant.

 

[hermy]

thanks everyone!

 

[Mentallic]

so, the answer would be 960 km/s.

960 km/h to be exact :tongue: