littlesmallworld
Member
- Joined
- Sep 5, 2013
- Messages
- 89
- Gender
- Female
- HSC
- 2014
1. A picture 1 metre tall is hung on a wall with its bottom edge 3 metres above the eye E of a viewer. Let the distance EP be x metres, and let theta be the angle that the picture subtends at E.
a) show that theta us maximised when the viewer is root 12 metres from the wall
b) show that the maximum angle subtended by the picture at E
is inverse tan (root3/12)
2. A plane P at an altitude of 6km and at a constant speed of 600km/h is flying directly away from the observer af O on the ground. A is the point on the path of the plane directly above O and the distance AP is xkm.
The angle of elevation of the plane from the observer is theta.
A) show that dtheta/dt = -3600/(x^2 + 36) radians per hour
B) hence find in radians per second, the rate at which theta is decreasing at the instant when the distance AP is 3km
Thanks very much
a) show that theta us maximised when the viewer is root 12 metres from the wall
b) show that the maximum angle subtended by the picture at E
is inverse tan (root3/12)
2. A plane P at an altitude of 6km and at a constant speed of 600km/h is flying directly away from the observer af O on the ground. A is the point on the path of the plane directly above O and the distance AP is xkm.
The angle of elevation of the plane from the observer is theta.
A) show that dtheta/dt = -3600/(x^2 + 36) radians per hour
B) hence find in radians per second, the rate at which theta is decreasing at the instant when the distance AP is 3km
Thanks very much
