# math cal

A plane flying horizontally at an altitude of 3 mi and a speed of 480 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. (Round to the nearest whole number.)

1. 👍 0
2. 👎 1
3. 👁 4,154
1. Did you make a sketch and got a right-angled triangle?
let the horizontal distance between the plane and the station be x miles
let the distance between the plane and the station be y miles
given: dx/dt = 480 mph
find: dy/dt when y = 6

y^2 = x^2 + 3^2
when y = 6
36 = x^2 + 9
x = √27

2y dy/dt = 2x dx/dt
dy/dt = (x/y)dx/dt
= √27(480)/6
= 415.7 mph or 416 mph

1. 👍 0
2. 👎 9
2. 64

1. 👍 1
2. 👎 2

## Similar Questions

1. ### Physics

A cargo plane is flying horizontally at an altitude of 10000m with a velocity of 800km/h when a cargo pallet falls out the back ramp. (i) How long does it take to fall to the ground? (ii) How far horizontally is the pallet from

2. ### math

A plane takes off at an angle of 20 degrees. Assuming a constant speed and trajectory, by the time it has travelled 25 kilometres horizontally, how high will it be flying?

3. ### calculus

A plane flying horizontally at an altitude of 1 mi and a speed of 560 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the

4. ### Physics

A ship fires its guns with a speed of 400 m/s at an angle of 35 with the horizontal. a. Find the range and maximum altitude. b. If the ship hits a plane that was 12 km away, how high was the plane flying?

1. ### Trigonometry

A plane is observed approaching your home and you assume its speed to be 550 miles per hour. The angle of elevation of the plane is 16 degrees and one minute later is 57 degrees. Approximate the altitude of the plane. Draw

2. ### Calculus

A plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the

3. ### geometry

An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?

4. ### calculus

A plane flies horizontally with a speed Of 600km/h at an altitude of 10km and pasess directly over th town of quinton .find the rate at which the distance from the plane to quinton is increasing when its 20km away from quinton ?

1. ### Cal

A plane flying horizontally at an altitude of 3 mi and a speed of 480 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the

2. ### Physics

A cargo plane is flying horizontally at an altitude of 11.2 km with a constant speed of 1260 km/hr when a large crate slides out of the rear of the plane. How long does it take the crate to hit the ground? The acceleration of

3. ### Math

Have you ever been on an airplane and heard the pilot say that the plane would be a little late because it would be flying into a strong headwind or that even though the plane was taking off a bit late, you would be making up time

4. ### Physics

A bomber is flying horizontally over level terrain at a speed of 250 m/s relative to the ground and at an altitude of 3.20 km. The bombardier releases one bomb. How far does the bomb travel horizontally between its release and its